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Simplifying -8x2 + 3x + 100 = 0 Reorder the terms: 100 + 3x + -8x2 = 0 Solving 100 + 3x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.5 + -0.375x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.375x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.375x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.375x + x2 = 0 + 12.5 -0.375x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.375x + x2 = 12.5 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 12.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 12.5 + 0.03515625 Combine like terms: 12.5 + 0.03515625 = 12.53515625 0.03515625 + -0.375x + x2 = 12.53515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 12.53515625 Calculate the square root of the right side: 3.54050226 Break this problem into two subproblems by setting (x + -0.1875) equal to 3.54050226 and -3.54050226.Subproblem 1
x + -0.1875 = 3.54050226 Simplifying x + -0.1875 = 3.54050226 Reorder the terms: -0.1875 + x = 3.54050226 Solving -0.1875 + x = 3.54050226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 3.54050226 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 3.54050226 + 0.1875 x = 3.54050226 + 0.1875 Combine like terms: 3.54050226 + 0.1875 = 3.72800226 x = 3.72800226 Simplifying x = 3.72800226Subproblem 2
x + -0.1875 = -3.54050226 Simplifying x + -0.1875 = -3.54050226 Reorder the terms: -0.1875 + x = -3.54050226 Solving -0.1875 + x = -3.54050226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -3.54050226 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -3.54050226 + 0.1875 x = -3.54050226 + 0.1875 Combine like terms: -3.54050226 + 0.1875 = -3.35300226 x = -3.35300226 Simplifying x = -3.35300226Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.72800226, -3.35300226}
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