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Simplifying -16x2 + -7x + 10 = 0 Reorder the terms: 10 + -7x + -16x2 = 0 Solving 10 + -7x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.625 + 0.4375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.4375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.4375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.4375x + x2 = 0 + 0.625 0.4375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.4375x + x2 = 0.625 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 = 0.625 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375x + x2 = 0.625 + 0.0478515625 Combine like terms: 0.625 + 0.0478515625 = 0.6728515625 0.0478515625 + 0.4375x + x2 = 0.6728515625 Factor a perfect square on the left side: (x + 0.21875)(x + 0.21875) = 0.6728515625 Calculate the square root of the right side: 0.820275297 Break this problem into two subproblems by setting (x + 0.21875) equal to 0.820275297 and -0.820275297.Subproblem 1
x + 0.21875 = 0.820275297 Simplifying x + 0.21875 = 0.820275297 Reorder the terms: 0.21875 + x = 0.820275297 Solving 0.21875 + x = 0.820275297 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 = 0.820275297 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = 0.820275297 + -0.21875 x = 0.820275297 + -0.21875 Combine like terms: 0.820275297 + -0.21875 = 0.601525297 x = 0.601525297 Simplifying x = 0.601525297Subproblem 2
x + 0.21875 = -0.820275297 Simplifying x + 0.21875 = -0.820275297 Reorder the terms: 0.21875 + x = -0.820275297 Solving 0.21875 + x = -0.820275297 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 = -0.820275297 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = -0.820275297 + -0.21875 x = -0.820275297 + -0.21875 Combine like terms: -0.820275297 + -0.21875 = -1.039025297 x = -1.039025297 Simplifying x = -1.039025297Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.601525297, -1.039025297}
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