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Simplifying 9 + -7x = 16x2 + -9 + 5 Reorder the terms: 9 + -7x = -9 + 5 + 16x2 Combine like terms: -9 + 5 = -4 9 + -7x = -4 + 16x2 Solving 9 + -7x = -4 + 16x2 Solving for variable 'x'. Reorder the terms: 9 + 4 + -7x + -16x2 = -4 + 16x2 + 4 + -16x2 Combine like terms: 9 + 4 = 13 13 + -7x + -16x2 = -4 + 16x2 + 4 + -16x2 Reorder the terms: 13 + -7x + -16x2 = -4 + 4 + 16x2 + -16x2 Combine like terms: -4 + 4 = 0 13 + -7x + -16x2 = 0 + 16x2 + -16x2 13 + -7x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 13 + -7x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.8125 + 0.4375x + x2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + 0.4375x + 0.8125 + x2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + 0.4375x + x2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + 0.4375x + x2 = 0 + 0.8125 0.4375x + x2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 0.4375x + x2 = 0.8125 The x term is 0.4375x. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375x + 0.0478515625 + x2 = 0.8125 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375x + x2 = 0.8125 + 0.0478515625 Combine like terms: 0.8125 + 0.0478515625 = 0.8603515625 0.0478515625 + 0.4375x + x2 = 0.8603515625 Factor a perfect square on the left side: (x + 0.21875)(x + 0.21875) = 0.8603515625 Calculate the square root of the right side: 0.92755138 Break this problem into two subproblems by setting (x + 0.21875) equal to 0.92755138 and -0.92755138.Subproblem 1
x + 0.21875 = 0.92755138 Simplifying x + 0.21875 = 0.92755138 Reorder the terms: 0.21875 + x = 0.92755138 Solving 0.21875 + x = 0.92755138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = 0.92755138 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = 0.92755138 + -0.21875 x = 0.92755138 + -0.21875 Combine like terms: 0.92755138 + -0.21875 = 0.70880138 x = 0.70880138 Simplifying x = 0.70880138Subproblem 2
x + 0.21875 = -0.92755138 Simplifying x + 0.21875 = -0.92755138 Reorder the terms: 0.21875 + x = -0.92755138 Solving 0.21875 + x = -0.92755138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = -0.92755138 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = -0.92755138 + -0.21875 x = -0.92755138 + -0.21875 Combine like terms: -0.92755138 + -0.21875 = -1.14630138 x = -1.14630138 Simplifying x = -1.14630138Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.70880138, -1.14630138}
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