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Simplifying 2x2 + -23x + 15 = 0 Reorder the terms: 15 + -23x + 2x2 = 0 Solving 15 + -23x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -11.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -11.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -11.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -11.5x + x2 = 0 + -7.5 -11.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -11.5x + x2 = -7.5 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -7.5 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -7.5 + 33.0625 Combine like terms: -7.5 + 33.0625 = 25.5625 33.0625 + -11.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -5.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -5.75 = 5.055937104 Simplifying x + -5.75 = 5.055937104 Reorder the terms: -5.75 + x = 5.055937104 Solving -5.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 5.055937104 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 5.055937104 + 5.75 x = 5.055937104 + 5.75 Combine like terms: 5.055937104 + 5.75 = 10.805937104 x = 10.805937104 Simplifying x = 10.805937104Subproblem 2
x + -5.75 = -5.055937104 Simplifying x + -5.75 = -5.055937104 Reorder the terms: -5.75 + x = -5.055937104 Solving -5.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -5.055937104 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -5.055937104 + 5.75 x = -5.055937104 + 5.75 Combine like terms: -5.055937104 + 5.75 = 0.694062896 x = 0.694062896 Simplifying x = 0.694062896Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.805937104, 0.694062896}
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