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Simplifying -0.8x2 + 14.4x + 12 = 0 Reorder the terms: 12 + 14.4x + -0.8x2 = 0 Solving 12 + 14.4x + -0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -15 + -18x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -18x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -18x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -18x + x2 = 0 + 15 -18x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -18x + x2 = 15 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 15 + 81 Reorder the terms: 81 + -18x + x2 = 15 + 81 Combine like terms: 15 + 81 = 96 81 + -18x + x2 = 96 Factor a perfect square on the left side: (x + -9)(x + -9) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -9) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -9 = 9.797958971 Simplifying x + -9 = 9.797958971 Reorder the terms: -9 + x = 9.797958971 Solving -9 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.797958971 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.797958971 + 9 x = 9.797958971 + 9 Combine like terms: 9.797958971 + 9 = 18.797958971 x = 18.797958971 Simplifying x = 18.797958971Subproblem 2
x + -9 = -9.797958971 Simplifying x + -9 = -9.797958971 Reorder the terms: -9 + x = -9.797958971 Solving -9 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.797958971 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.797958971 + 9 x = -9.797958971 + 9 Combine like terms: -9.797958971 + 9 = -0.797958971 x = -0.797958971 Simplifying x = -0.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.797958971, -0.797958971}
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