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Simplifying -5x2 + 3 = 14x2 + -8x Reorder the terms: 3 + -5x2 = 14x2 + -8x Reorder the terms: 3 + -5x2 = -8x + 14x2 Solving 3 + -5x2 = -8x + 14x2 Solving for variable 'x'. Reorder the terms: 3 + 8x + -5x2 + -14x2 = -8x + 14x2 + 8x + -14x2 Combine like terms: -5x2 + -14x2 = -19x2 3 + 8x + -19x2 = -8x + 14x2 + 8x + -14x2 Reorder the terms: 3 + 8x + -19x2 = -8x + 8x + 14x2 + -14x2 Combine like terms: -8x + 8x = 0 3 + 8x + -19x2 = 0 + 14x2 + -14x2 3 + 8x + -19x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 3 + 8x + -19x2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.1578947368 + -0.4210526316x + x2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + -0.4210526316x + 0.1578947368 + x2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + -0.4210526316x + x2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + -0.4210526316x + x2 = 0 + 0.1578947368 -0.4210526316x + x2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 -0.4210526316x + x2 = 0.1578947368 The x term is -0.4210526316x. Take half its coefficient (-0.2105263158). Square it (0.04432132964) and add it to both sides. Add '0.04432132964' to each side of the equation. -0.4210526316x + 0.04432132964 + x2 = 0.1578947368 + 0.04432132964 Reorder the terms: 0.04432132964 + -0.4210526316x + x2 = 0.1578947368 + 0.04432132964 Combine like terms: 0.1578947368 + 0.04432132964 = 0.20221606644 0.04432132964 + -0.4210526316x + x2 = 0.20221606644 Factor a perfect square on the left side: (x + -0.2105263158)(x + -0.2105263158) = 0.20221606644 Calculate the square root of the right side: 0.449684408 Break this problem into two subproblems by setting (x + -0.2105263158) equal to 0.449684408 and -0.449684408.Subproblem 1
x + -0.2105263158 = 0.449684408 Simplifying x + -0.2105263158 = 0.449684408 Reorder the terms: -0.2105263158 + x = 0.449684408 Solving -0.2105263158 + x = 0.449684408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2105263158' to each side of the equation. -0.2105263158 + 0.2105263158 + x = 0.449684408 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + x = 0.449684408 + 0.2105263158 x = 0.449684408 + 0.2105263158 Combine like terms: 0.449684408 + 0.2105263158 = 0.6602107238 x = 0.6602107238 Simplifying x = 0.6602107238Subproblem 2
x + -0.2105263158 = -0.449684408 Simplifying x + -0.2105263158 = -0.449684408 Reorder the terms: -0.2105263158 + x = -0.449684408 Solving -0.2105263158 + x = -0.449684408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2105263158' to each side of the equation. -0.2105263158 + 0.2105263158 + x = -0.449684408 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + x = -0.449684408 + 0.2105263158 x = -0.449684408 + 0.2105263158 Combine like terms: -0.449684408 + 0.2105263158 = -0.2391580922 x = -0.2391580922 Simplifying x = -0.2391580922Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6602107238, -0.2391580922}
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