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Simplifying -0.01x2 + 0.24x + -0.95 = 0 Reorder the terms: -0.95 + 0.24x + -0.01x2 = 0 Solving -0.95 + 0.24x + -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'. 95 + -24x + x2 = 0 Move the constant term to the right: Add '-95' to each side of the equation. 95 + -24x + -95 + x2 = 0 + -95 Reorder the terms: 95 + -95 + -24x + x2 = 0 + -95 Combine like terms: 95 + -95 = 0 0 + -24x + x2 = 0 + -95 -24x + x2 = 0 + -95 Combine like terms: 0 + -95 = -95 -24x + x2 = -95 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -95 + 144 Reorder the terms: 144 + -24x + x2 = -95 + 144 Combine like terms: -95 + 144 = 49 144 + -24x + x2 = 49 Factor a perfect square on the left side: (x + -12)(x + -12) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + -12) equal to 7 and -7.Subproblem 1
x + -12 = 7 Simplifying x + -12 = 7 Reorder the terms: -12 + x = 7 Solving -12 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 7 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7 + 12 x = 7 + 12 Combine like terms: 7 + 12 = 19 x = 19 Simplifying x = 19Subproblem 2
x + -12 = -7 Simplifying x + -12 = -7 Reorder the terms: -12 + x = -7 Solving -12 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -7 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7 + 12 x = -7 + 12 Combine like terms: -7 + 12 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {19, 5}
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