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Simplifying -54 = -0.8x2 + 14.4x + 2 Reorder the terms: -54 = 2 + 14.4x + -0.8x2 Solving -54 = 2 + 14.4x + -0.8x2 Solving for variable 'x'. Combine like terms: -54 + -2 = -56 -56 + -14.4x + 0.8x2 = 2 + 14.4x + -0.8x2 + -2 + -14.4x + 0.8x2 Reorder the terms: -56 + -14.4x + 0.8x2 = 2 + -2 + 14.4x + -14.4x + -0.8x2 + 0.8x2 Combine like terms: 2 + -2 = 0 -56 + -14.4x + 0.8x2 = 0 + 14.4x + -14.4x + -0.8x2 + 0.8x2 -56 + -14.4x + 0.8x2 = 14.4x + -14.4x + -0.8x2 + 0.8x2 Combine like terms: 14.4x + -14.4x = 0.0 -56 + -14.4x + 0.8x2 = 0.0 + -0.8x2 + 0.8x2 -56 + -14.4x + 0.8x2 = -0.8x2 + 0.8x2 Combine like terms: -0.8x2 + 0.8x2 = 0.0 -56 + -14.4x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -70 + -18x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -18x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -18x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -18x + x2 = 0 + 70 -18x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -18x + x2 = 70 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 = 70 + 81 Reorder the terms: 81 + -18x + x2 = 70 + 81 Combine like terms: 70 + 81 = 151 81 + -18x + x2 = 151 Factor a perfect square on the left side: (x + -9)(x + -9) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + -9) equal to 12.288205727 and -12.288205727.Subproblem 1
x + -9 = 12.288205727 Simplifying x + -9 = 12.288205727 Reorder the terms: -9 + x = 12.288205727 Solving -9 + x = 12.288205727 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 = 12.288205727 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.288205727 + 9 x = 12.288205727 + 9 Combine like terms: 12.288205727 + 9 = 21.288205727 x = 21.288205727 Simplifying x = 21.288205727Subproblem 2
x + -9 = -12.288205727 Simplifying x + -9 = -12.288205727 Reorder the terms: -9 + x = -12.288205727 Solving -9 + x = -12.288205727 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 = -12.288205727 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.288205727 + 9 x = -12.288205727 + 9 Combine like terms: -12.288205727 + 9 = -3.288205727 x = -3.288205727 Simplifying x = -3.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.288205727, -3.288205727}
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