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Simplifying 8x2 + 19x + -100 = 0 Reorder the terms: -100 + 19x + 8x2 = 0 Solving -100 + 19x + 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 + 2.375x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 2.375x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 2.375x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 2.375x + x2 = 0 + 12.5 2.375x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 2.375x + x2 = 12.5 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = 12.5 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 12.5 + 1.41015625 Combine like terms: 12.5 + 1.41015625 = 13.91015625 1.41015625 + 2.375x + x2 = 13.91015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 13.91015625 Calculate the square root of the right side: 3.729632187 Break this problem into two subproblems by setting (x + 1.1875) equal to 3.729632187 and -3.729632187.Subproblem 1
x + 1.1875 = 3.729632187 Simplifying x + 1.1875 = 3.729632187 Reorder the terms: 1.1875 + x = 3.729632187 Solving 1.1875 + x = 3.729632187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 3.729632187 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 3.729632187 + -1.1875 x = 3.729632187 + -1.1875 Combine like terms: 3.729632187 + -1.1875 = 2.542132187 x = 2.542132187 Simplifying x = 2.542132187Subproblem 2
x + 1.1875 = -3.729632187 Simplifying x + 1.1875 = -3.729632187 Reorder the terms: 1.1875 + x = -3.729632187 Solving 1.1875 + x = -3.729632187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -3.729632187 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -3.729632187 + -1.1875 x = -3.729632187 + -1.1875 Combine like terms: -3.729632187 + -1.1875 = -4.917132187 x = -4.917132187 Simplifying x = -4.917132187Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.542132187, -4.917132187}
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