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Simplifying 9x2 + 15x = 52 Reorder the terms: 15x + 9x2 = 52 Solving 15x + 9x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 15x + 9x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 15x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.777777778 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '5.777777778' to each side of the equation. -5.777777778 + 1.666666667x + 5.777777778 + x2 = 0 + 5.777777778 Reorder the terms: -5.777777778 + 5.777777778 + 1.666666667x + x2 = 0 + 5.777777778 Combine like terms: -5.777777778 + 5.777777778 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 5.777777778 1.666666667x + x2 = 0 + 5.777777778 Combine like terms: 0 + 5.777777778 = 5.777777778 1.666666667x + x2 = 5.777777778 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 5.777777778 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 5.777777778 + 0.6944444447 Combine like terms: 5.777777778 + 0.6944444447 = 6.4722222227 0.6944444447 + 1.666666667x + x2 = 6.4722222227 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 6.4722222227 Calculate the square root of the right side: 2.544056254 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.544056254 and -2.544056254.Subproblem 1
x + 0.8333333335 = 2.544056254 Simplifying x + 0.8333333335 = 2.544056254 Reorder the terms: 0.8333333335 + x = 2.544056254 Solving 0.8333333335 + x = 2.544056254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.544056254 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.544056254 + -0.8333333335 x = 2.544056254 + -0.8333333335 Combine like terms: 2.544056254 + -0.8333333335 = 1.7107229205 x = 1.7107229205 Simplifying x = 1.7107229205Subproblem 2
x + 0.8333333335 = -2.544056254 Simplifying x + 0.8333333335 = -2.544056254 Reorder the terms: 0.8333333335 + x = -2.544056254 Solving 0.8333333335 + x = -2.544056254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.544056254 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.544056254 + -0.8333333335 x = -2.544056254 + -0.8333333335 Combine like terms: -2.544056254 + -0.8333333335 = -3.3773895875 x = -3.3773895875 Simplifying x = -3.3773895875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7107229205, -3.3773895875}
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