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Simplifying (5x2 + 9x + 9) + (-8x2 + -3x + 7) + -1(7x2 + -4x + -7) = 0 Reorder the terms: (9 + 9x + 5x2) + (-8x2 + -3x + 7) + -1(7x2 + -4x + -7) = 0 Remove parenthesis around (9 + 9x + 5x2) 9 + 9x + 5x2 + (-8x2 + -3x + 7) + -1(7x2 + -4x + -7) = 0 Reorder the terms: 9 + 9x + 5x2 + (7 + -3x + -8x2) + -1(7x2 + -4x + -7) = 0 Remove parenthesis around (7 + -3x + -8x2) 9 + 9x + 5x2 + 7 + -3x + -8x2 + -1(7x2 + -4x + -7) = 0 Reorder the terms: 9 + 9x + 5x2 + 7 + -3x + -8x2 + -1(-7 + -4x + 7x2) = 0 9 + 9x + 5x2 + 7 + -3x + -8x2 + (-7 * -1 + -4x * -1 + 7x2 * -1) = 0 9 + 9x + 5x2 + 7 + -3x + -8x2 + (7 + 4x + -7x2) = 0 Reorder the terms: 9 + 7 + 7 + 9x + -3x + 4x + 5x2 + -8x2 + -7x2 = 0 Combine like terms: 9 + 7 = 16 16 + 7 + 9x + -3x + 4x + 5x2 + -8x2 + -7x2 = 0 Combine like terms: 16 + 7 = 23 23 + 9x + -3x + 4x + 5x2 + -8x2 + -7x2 = 0 Combine like terms: 9x + -3x = 6x 23 + 6x + 4x + 5x2 + -8x2 + -7x2 = 0 Combine like terms: 6x + 4x = 10x 23 + 10x + 5x2 + -8x2 + -7x2 = 0 Combine like terms: 5x2 + -8x2 = -3x2 23 + 10x + -3x2 + -7x2 = 0 Combine like terms: -3x2 + -7x2 = -10x2 23 + 10x + -10x2 = 0 Solving 23 + 10x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.3 + -1x + x2 = 0.0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + -1x + 2.3 + x2 = 0.0 + 2.3 Reorder the terms: -2.3 + 2.3 + -1x + x2 = 0.0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + -1x + x2 = 0.0 + 2.3 -1x + x2 = 0.0 + 2.3 Combine like terms: 0.0 + 2.3 = 2.3 -1x + x2 = 2.3 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.3 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.3 + 0.25 Combine like terms: 2.3 + 0.25 = 2.55 0.25 + -1x + x2 = 2.55 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.55 Calculate the square root of the right side: 1.596871942 Break this problem into two subproblems by setting (x + -0.5) equal to 1.596871942 and -1.596871942.Subproblem 1
x + -0.5 = 1.596871942 Simplifying x + -0.5 = 1.596871942 Reorder the terms: -0.5 + x = 1.596871942 Solving -0.5 + x = 1.596871942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.596871942 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.596871942 + 0.5 x = 1.596871942 + 0.5 Combine like terms: 1.596871942 + 0.5 = 2.096871942 x = 2.096871942 Simplifying x = 2.096871942Subproblem 2
x + -0.5 = -1.596871942 Simplifying x + -0.5 = -1.596871942 Reorder the terms: -0.5 + x = -1.596871942 Solving -0.5 + x = -1.596871942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.596871942 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.596871942 + 0.5 x = -1.596871942 + 0.5 Combine like terms: -1.596871942 + 0.5 = -1.096871942 x = -1.096871942 Simplifying x = -1.096871942Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.096871942, -1.096871942}
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