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Simplifying 17x2 + 14x + -13 = 2x2 + -1 Reorder the terms: -13 + 14x + 17x2 = 2x2 + -1 Reorder the terms: -13 + 14x + 17x2 = -1 + 2x2 Solving -13 + 14x + 17x2 = -1 + 2x2 Solving for variable 'x'. Reorder the terms: -13 + 1 + 14x + 17x2 + -2x2 = -1 + 2x2 + 1 + -2x2 Combine like terms: -13 + 1 = -12 -12 + 14x + 17x2 + -2x2 = -1 + 2x2 + 1 + -2x2 Combine like terms: 17x2 + -2x2 = 15x2 -12 + 14x + 15x2 = -1 + 2x2 + 1 + -2x2 Reorder the terms: -12 + 14x + 15x2 = -1 + 1 + 2x2 + -2x2 Combine like terms: -1 + 1 = 0 -12 + 14x + 15x2 = 0 + 2x2 + -2x2 -12 + 14x + 15x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 14x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + 0.9333333333x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.9333333333x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.9333333333x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.9333333333x + x2 = 0 + 0.8 0.9333333333x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.9333333333x + x2 = 0.8 The x term is 0.9333333333x. Take half its coefficient (0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. 0.9333333333x + 0.2177777778 + x2 = 0.8 + 0.2177777778 Reorder the terms: 0.2177777778 + 0.9333333333x + x2 = 0.8 + 0.2177777778 Combine like terms: 0.8 + 0.2177777778 = 1.0177777778 0.2177777778 + 0.9333333333x + x2 = 1.0177777778 Factor a perfect square on the left side: (x + 0.4666666667)(x + 0.4666666667) = 1.0177777778 Calculate the square root of the right side: 1.00884973 Break this problem into two subproblems by setting (x + 0.4666666667) equal to 1.00884973 and -1.00884973.Subproblem 1
x + 0.4666666667 = 1.00884973 Simplifying x + 0.4666666667 = 1.00884973 Reorder the terms: 0.4666666667 + x = 1.00884973 Solving 0.4666666667 + x = 1.00884973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 1.00884973 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 1.00884973 + -0.4666666667 x = 1.00884973 + -0.4666666667 Combine like terms: 1.00884973 + -0.4666666667 = 0.5421830633 x = 0.5421830633 Simplifying x = 0.5421830633Subproblem 2
x + 0.4666666667 = -1.00884973 Simplifying x + 0.4666666667 = -1.00884973 Reorder the terms: 0.4666666667 + x = -1.00884973 Solving 0.4666666667 + x = -1.00884973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -1.00884973 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -1.00884973 + -0.4666666667 x = -1.00884973 + -0.4666666667 Combine like terms: -1.00884973 + -0.4666666667 = -1.4755163967 x = -1.4755163967 Simplifying x = -1.4755163967Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5421830633, -1.4755163967}
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