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Simplifying 10 = 0.1x2 + 2.4x + 8.1 Reorder the terms: 10 = 8.1 + 2.4x + 0.1x2 Solving 10 = 8.1 + 2.4x + 0.1x2 Solving for variable 'x'. Combine like terms: 10 + -8.1 = 1.9 1.9 + -2.4x + -0.1x2 = 8.1 + 2.4x + 0.1x2 + -8.1 + -2.4x + -0.1x2 Reorder the terms: 1.9 + -2.4x + -0.1x2 = 8.1 + -8.1 + 2.4x + -2.4x + 0.1x2 + -0.1x2 Combine like terms: 8.1 + -8.1 = 0.0 1.9 + -2.4x + -0.1x2 = 0.0 + 2.4x + -2.4x + 0.1x2 + -0.1x2 1.9 + -2.4x + -0.1x2 = 2.4x + -2.4x + 0.1x2 + -0.1x2 Combine like terms: 2.4x + -2.4x = 0.0 1.9 + -2.4x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 1.9 + -2.4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 1.9 + -2.4x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -19 + 24x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 24x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 24x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 24x + x2 = 0 + 19 24x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 24x + x2 = 19 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 19 + 144 Reorder the terms: 144 + 24x + x2 = 19 + 144 Combine like terms: 19 + 144 = 163 144 + 24x + x2 = 163 Factor a perfect square on the left side: (x + 12)(x + 12) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 12) equal to 12.767145335 and -12.767145335.Subproblem 1
x + 12 = 12.767145335 Simplifying x + 12 = 12.767145335 Reorder the terms: 12 + x = 12.767145335 Solving 12 + x = 12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.767145335 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.767145335 + -12 x = 12.767145335 + -12 Combine like terms: 12.767145335 + -12 = 0.767145335 x = 0.767145335 Simplifying x = 0.767145335Subproblem 2
x + 12 = -12.767145335 Simplifying x + 12 = -12.767145335 Reorder the terms: 12 + x = -12.767145335 Solving 12 + x = -12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.767145335 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.767145335 + -12 x = -12.767145335 + -12 Combine like terms: -12.767145335 + -12 = -24.767145335 x = -24.767145335 Simplifying x = -24.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.767145335, -24.767145335}
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