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Simplifying 2x2 + -9 + -4x2 + -8x + 49 = -4x Reorder the terms: -9 + 49 + -8x + 2x2 + -4x2 = -4x Combine like terms: -9 + 49 = 40 40 + -8x + 2x2 + -4x2 = -4x Combine like terms: 2x2 + -4x2 = -2x2 40 + -8x + -2x2 = -4x Solving 40 + -8x + -2x2 = -4x Solving for variable 'x'. Reorder the terms: 40 + -8x + 4x + -2x2 = -4x + 4x Combine like terms: -8x + 4x = -4x 40 + -4x + -2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 40 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 20 + -2x + -1x2 = 0 Solving 20 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 2x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2x + x2 = 0 + 20 2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 2x + x2 = 20 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 20 + 1 Reorder the terms: 1 + 2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2x + x2 = 21 Factor a perfect square on the left side: (x + 1)(x + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 1 = 4.582575695 Simplifying x + 1 = 4.582575695 Reorder the terms: 1 + x = 4.582575695 Solving 1 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.582575695 + -1 x = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 x = 3.582575695 Simplifying x = 3.582575695Subproblem 2
x + 1 = -4.582575695 Simplifying x + 1 = -4.582575695 Reorder the terms: 1 + x = -4.582575695 Solving 1 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.582575695 + -1 x = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 x = -5.582575695 Simplifying x = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.582575695, -5.582575695}Solution
x = {3.582575695, -5.582575695}
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