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Simplifying 90 = 24x + -0.8x2 Solving 90 = 24x + -0.8x2 Solving for variable 'x'. Reorder the terms: 90 + -24x + 0.8x2 = 24x + -24x + -0.8x2 + 0.8x2 Combine like terms: 24x + -24x = 0 90 + -24x + 0.8x2 = 0 + -0.8x2 + 0.8x2 90 + -24x + 0.8x2 = -0.8x2 + 0.8x2 Combine like terms: -0.8x2 + 0.8x2 = 0.0 90 + -24x + 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'. 112.5 + -30x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -30x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -30x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -30x + x2 = 0 + -112.5 -30x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -30x + x2 = -112.5 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -112.5 + 225 Reorder the terms: 225 + -30x + x2 = -112.5 + 225 Combine like terms: -112.5 + 225 = 112.5 225 + -30x + x2 = 112.5 Factor a perfect square on the left side: (x + -15)(x + -15) = 112.5 Calculate the square root of the right side: 10.606601718 Break this problem into two subproblems by setting (x + -15) equal to 10.606601718 and -10.606601718.Subproblem 1
x + -15 = 10.606601718 Simplifying x + -15 = 10.606601718 Reorder the terms: -15 + x = 10.606601718 Solving -15 + x = 10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + x = 10.606601718 + 15 x = 10.606601718 + 15 Combine like terms: 10.606601718 + 15 = 25.606601718 x = 25.606601718 Simplifying x = 25.606601718Subproblem 2
x + -15 = -10.606601718 Simplifying x + -15 = -10.606601718 Reorder the terms: -15 + x = -10.606601718 Solving -15 + x = -10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + x = -10.606601718 + 15 x = -10.606601718 + 15 Combine like terms: -10.606601718 + 15 = 4.393398282 x = 4.393398282 Simplifying x = 4.393398282Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.606601718, 4.393398282}
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