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Simplifying 5x(x + 9) + -6(x + -7) = 0 Reorder the terms: 5x(9 + x) + -6(x + -7) = 0 (9 * 5x + x * 5x) + -6(x + -7) = 0 (45x + 5x2) + -6(x + -7) = 0 Reorder the terms: 45x + 5x2 + -6(-7 + x) = 0 45x + 5x2 + (-7 * -6 + x * -6) = 0 45x + 5x2 + (42 + -6x) = 0 Reorder the terms: 42 + 45x + -6x + 5x2 = 0 Combine like terms: 45x + -6x = 39x 42 + 39x + 5x2 = 0 Solving 42 + 39x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + 7.8x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 7.8x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 7.8x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 7.8x + x2 = 0 + -8.4 7.8x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 7.8x + x2 = -8.4 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -8.4 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -8.4 + 15.21 Combine like terms: -8.4 + 15.21 = 6.81 15.21 + 7.8x + x2 = 6.81 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 6.81 Calculate the square root of the right side: 2.60959767 Break this problem into two subproblems by setting (x + 3.9) equal to 2.60959767 and -2.60959767.Subproblem 1
x + 3.9 = 2.60959767 Simplifying x + 3.9 = 2.60959767 Reorder the terms: 3.9 + x = 2.60959767 Solving 3.9 + x = 2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 2.60959767 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 2.60959767 + -3.9 x = 2.60959767 + -3.9 Combine like terms: 2.60959767 + -3.9 = -1.29040233 x = -1.29040233 Simplifying x = -1.29040233Subproblem 2
x + 3.9 = -2.60959767 Simplifying x + 3.9 = -2.60959767 Reorder the terms: 3.9 + x = -2.60959767 Solving 3.9 + x = -2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -2.60959767 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -2.60959767 + -3.9 x = -2.60959767 + -3.9 Combine like terms: -2.60959767 + -3.9 = -6.50959767 x = -6.50959767 Simplifying x = -6.50959767Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.29040233, -6.50959767}
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