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Simplifying 22.5 = 0.8x2 + 12x Reorder the terms: 22.5 = 12x + 0.8x2 Solving 22.5 = 12x + 0.8x2 Solving for variable 'x'. Reorder the terms: 22.5 + -12x + -0.8x2 = 12x + -12x + 0.8x2 + -0.8x2 Combine like terms: 12x + -12x = 0 22.5 + -12x + -0.8x2 = 0 + 0.8x2 + -0.8x2 22.5 + -12x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 22.5 + -12x + -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'. -28.125 + 15x + x2 = 0 Move the constant term to the right: Add '28.125' to each side of the equation. -28.125 + 15x + 28.125 + x2 = 0 + 28.125 Reorder the terms: -28.125 + 28.125 + 15x + x2 = 0 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + 15x + x2 = 0 + 28.125 15x + x2 = 0 + 28.125 Combine like terms: 0 + 28.125 = 28.125 15x + x2 = 28.125 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 28.125 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 28.125 + 56.25 Combine like terms: 28.125 + 56.25 = 84.375 56.25 + 15x + x2 = 84.375 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 84.375 Calculate the square root of the right side: 9.185586535 Break this problem into two subproblems by setting (x + 7.5) equal to 9.185586535 and -9.185586535.Subproblem 1
x + 7.5 = 9.185586535 Simplifying x + 7.5 = 9.185586535 Reorder the terms: 7.5 + x = 9.185586535 Solving 7.5 + x = 9.185586535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.185586535 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.185586535 + -7.5 x = 9.185586535 + -7.5 Combine like terms: 9.185586535 + -7.5 = 1.685586535 x = 1.685586535 Simplifying x = 1.685586535Subproblem 2
x + 7.5 = -9.185586535 Simplifying x + 7.5 = -9.185586535 Reorder the terms: 7.5 + x = -9.185586535 Solving 7.5 + x = -9.185586535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.185586535 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.185586535 + -7.5 x = -9.185586535 + -7.5 Combine like terms: -9.185586535 + -7.5 = -16.685586535 x = -16.685586535 Simplifying x = -16.685586535Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.685586535, -16.685586535}
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