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Simplifying [(5x2 + -3x + 3) + -1(4x2 + 6x + -3)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Reorder the terms: [(3 + -3x + 5x2) + -1(4x2 + 6x + -3)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Remove parenthesis around (3 + -3x + 5x2) [3 + -3x + 5x2 + -1(4x2 + 6x + -3)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Reorder the terms: [3 + -3x + 5x2 + -1(-3 + 6x + 4x2)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 [3 + -3x + 5x2 + (-3 * -1 + 6x * -1 + 4x2 * -1)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 [3 + -3x + 5x2 + (3 + -6x + -4x2)] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Reorder the terms: [3 + 3 + -3x + -6x + 5x2 + -4x2] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Combine like terms: 3 + 3 = 6 [6 + -3x + -6x + 5x2 + -4x2] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Combine like terms: -3x + -6x = -9x [6 + -9x + 5x2 + -4x2] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Combine like terms: 5x2 + -4x2 = 1x2 [6 + -9x + 1x2] + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Remove brackets around [6 + -9x + 1x2] 6 + -9x + 1x2 + -1[(6x2 + 6x + -5) + (-3x2 + 2x + 7)] = 0 Reorder the terms: 6 + -9x + 1x2 + -1[(-5 + 6x + 6x2) + (-3x2 + 2x + 7)] = 0 Remove parenthesis around (-5 + 6x + 6x2) 6 + -9x + 1x2 + -1[-5 + 6x + 6x2 + (-3x2 + 2x + 7)] = 0 Reorder the terms: 6 + -9x + 1x2 + -1[-5 + 6x + 6x2 + (7 + 2x + -3x2)] = 0 Remove parenthesis around (7 + 2x + -3x2) 6 + -9x + 1x2 + -1[-5 + 6x + 6x2 + 7 + 2x + -3x2] = 0 Reorder the terms: 6 + -9x + 1x2 + -1[-5 + 7 + 6x + 2x + 6x2 + -3x2] = 0 Combine like terms: -5 + 7 = 2 6 + -9x + 1x2 + -1[2 + 6x + 2x + 6x2 + -3x2] = 0 Combine like terms: 6x + 2x = 8x 6 + -9x + 1x2 + -1[2 + 8x + 6x2 + -3x2] = 0 Combine like terms: 6x2 + -3x2 = 3x2 6 + -9x + 1x2 + -1[2 + 8x + 3x2] = 0 6 + -9x + 1x2 + [2 * -1 + 8x * -1 + 3x2 * -1] = 0 6 + -9x + 1x2 + [-2 + -8x + -3x2] = 0 Reorder the terms: 6 + -2 + -9x + -8x + 1x2 + -3x2 = 0 Combine like terms: 6 + -2 = 4 4 + -9x + -8x + 1x2 + -3x2 = 0 Combine like terms: -9x + -8x = -17x 4 + -17x + 1x2 + -3x2 = 0 Combine like terms: 1x2 + -3x2 = -2x2 4 + -17x + -2x2 = 0 Solving 4 + -17x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + 8.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 8.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 8.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8.5x + x2 = 0 + 2 8.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 8.5x + x2 = 2 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 2 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 2 + 18.0625 Combine like terms: 2 + 18.0625 = 20.0625 18.0625 + 8.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 4.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 4.25 = 4.479118217 Simplifying x + 4.25 = 4.479118217 Reorder the terms: 4.25 + x = 4.479118217 Solving 4.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.479118217 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.479118217 + -4.25 x = 4.479118217 + -4.25 Combine like terms: 4.479118217 + -4.25 = 0.229118217 x = 0.229118217 Simplifying x = 0.229118217Subproblem 2
x + 4.25 = -4.479118217 Simplifying x + 4.25 = -4.479118217 Reorder the terms: 4.25 + x = -4.479118217 Solving 4.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.479118217 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.479118217 + -4.25 x = -4.479118217 + -4.25 Combine like terms: -4.479118217 + -4.25 = -8.729118217 x = -8.729118217 Simplifying x = -8.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.229118217, -8.729118217}
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