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Simplifying 7x2 + 9x = 132 Reorder the terms: 9x + 7x2 = 132 Solving 9x + 7x2 = 132 Solving for variable 'x'. Reorder the terms: -132 + 9x + 7x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -132 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -18.85714286 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '18.85714286' to each side of the equation. -18.85714286 + 1.285714286x + 18.85714286 + x2 = 0 + 18.85714286 Reorder the terms: -18.85714286 + 18.85714286 + 1.285714286x + x2 = 0 + 18.85714286 Combine like terms: -18.85714286 + 18.85714286 = 0.00000000 0.00000000 + 1.285714286x + x2 = 0 + 18.85714286 1.285714286x + x2 = 0 + 18.85714286 Combine like terms: 0 + 18.85714286 = 18.85714286 1.285714286x + x2 = 18.85714286 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 18.85714286 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 18.85714286 + 0.4132653063 Combine like terms: 18.85714286 + 0.4132653063 = 19.2704081663 0.4132653063 + 1.285714286x + x2 = 19.2704081663 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 19.2704081663 Calculate the square root of the right side: 4.389807304 Break this problem into two subproblems by setting (x + 0.642857143) equal to 4.389807304 and -4.389807304.Subproblem 1
x + 0.642857143 = 4.389807304 Simplifying x + 0.642857143 = 4.389807304 Reorder the terms: 0.642857143 + x = 4.389807304 Solving 0.642857143 + x = 4.389807304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 4.389807304 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 4.389807304 + -0.642857143 x = 4.389807304 + -0.642857143 Combine like terms: 4.389807304 + -0.642857143 = 3.746950161 x = 3.746950161 Simplifying x = 3.746950161Subproblem 2
x + 0.642857143 = -4.389807304 Simplifying x + 0.642857143 = -4.389807304 Reorder the terms: 0.642857143 + x = -4.389807304 Solving 0.642857143 + x = -4.389807304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -4.389807304 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -4.389807304 + -0.642857143 x = -4.389807304 + -0.642857143 Combine like terms: -4.389807304 + -0.642857143 = -5.032664447 x = -5.032664447 Simplifying x = -5.032664447Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.746950161, -5.032664447}
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