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Simplifying -0.01x2 + 0.23x + 8.8 = 9.7 Reorder the terms: 8.8 + 0.23x + -0.01x2 = 9.7 Solving 8.8 + 0.23x + -0.01x2 = 9.7 Solving for variable 'x'. Reorder the terms: 8.8 + -9.7 + 0.23x + -0.01x2 = 9.7 + -9.7 Combine like terms: 8.8 + -9.7 = -0.9 -0.9 + 0.23x + -0.01x2 = 9.7 + -9.7 Combine like terms: 9.7 + -9.7 = 0.0 -0.9 + 0.23x + -0.01x2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 90 + -23x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -23x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -23x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -23x + x2 = 0 + -90 -23x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -23x + x2 = -90 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -90 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -90 + 132.25 Combine like terms: -90 + 132.25 = 42.25 132.25 + -23x + x2 = 42.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + -11.5) equal to 6.5 and -6.5.Subproblem 1
x + -11.5 = 6.5 Simplifying x + -11.5 = 6.5 Reorder the terms: -11.5 + x = 6.5 Solving -11.5 + x = 6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 6.5 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 6.5 + 11.5 x = 6.5 + 11.5 Combine like terms: 6.5 + 11.5 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -11.5 = -6.5 Simplifying x + -11.5 = -6.5 Reorder the terms: -11.5 + x = -6.5 Solving -11.5 + x = -6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -6.5 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -6.5 + 11.5 x = -6.5 + 11.5 Combine like terms: -6.5 + 11.5 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, 5}
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