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Simplifying -16x2 + 15x + 100 = 0 Reorder the terms: 100 + 15x + -16x2 = 0 Solving 100 + 15x + -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'. -6.25 + -0.9375x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -0.9375x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -0.9375x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -0.9375x + x2 = 0 + 6.25 -0.9375x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -0.9375x + x2 = 6.25 The x term is -0.9375x. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375x + 0.2197265625 + x2 = 6.25 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 6.25 + 0.2197265625 Combine like terms: 6.25 + 0.2197265625 = 6.4697265625 0.2197265625 + -0.9375x + x2 = 6.4697265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 6.4697265625 Calculate the square root of the right side: 2.543565718 Break this problem into two subproblems by setting (x + -0.46875) equal to 2.543565718 and -2.543565718.Subproblem 1
x + -0.46875 = 2.543565718 Simplifying x + -0.46875 = 2.543565718 Reorder the terms: -0.46875 + x = 2.543565718 Solving -0.46875 + x = 2.543565718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = 2.543565718 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 2.543565718 + 0.46875 x = 2.543565718 + 0.46875 Combine like terms: 2.543565718 + 0.46875 = 3.012315718 x = 3.012315718 Simplifying x = 3.012315718Subproblem 2
x + -0.46875 = -2.543565718 Simplifying x + -0.46875 = -2.543565718 Reorder the terms: -0.46875 + x = -2.543565718 Solving -0.46875 + x = -2.543565718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = -2.543565718 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -2.543565718 + 0.46875 x = -2.543565718 + 0.46875 Combine like terms: -2.543565718 + 0.46875 = -2.074815718 x = -2.074815718 Simplifying x = -2.074815718Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.012315718, -2.074815718}
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