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Simplifying -0.01x2 + 0.25x + -1.5 = 0 Reorder the terms: -1.5 + 0.25x + -0.01x2 = 0 Solving -1.5 + 0.25x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 150 + -25x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -25x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -25x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -25x + x2 = 0 + -150 -25x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -25x + x2 = -150 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -150 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -150 + 156.25 Combine like terms: -150 + 156.25 = 6.25 156.25 + -25x + x2 = 6.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -12.5) equal to 2.5 and -2.5.Subproblem 1
x + -12.5 = 2.5 Simplifying x + -12.5 = 2.5 Reorder the terms: -12.5 + x = 2.5 Solving -12.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 2.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 2.5 + 12.5 x = 2.5 + 12.5 Combine like terms: 2.5 + 12.5 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -12.5 = -2.5 Simplifying x + -12.5 = -2.5 Reorder the terms: -12.5 + x = -2.5 Solving -12.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -2.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -2.5 + 12.5 x = -2.5 + 12.5 Combine like terms: -2.5 + 12.5 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, 10}
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