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Simplifying 5x2 + -8x + -23 = 0 Reorder the terms: -23 + -8x + 5x2 = 0 Solving -23 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + -1.6x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -1.6x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -1.6x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -1.6x + x2 = 0 + 4.6 -1.6x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -1.6x + x2 = 4.6 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 4.6 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 4.6 + 0.64 Combine like terms: 4.6 + 0.64 = 5.24 0.64 + -1.6x + x2 = 5.24 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 5.24 Calculate the square root of the right side: 2.289104628 Break this problem into two subproblems by setting (x + -0.8) equal to 2.289104628 and -2.289104628.Subproblem 1
x + -0.8 = 2.289104628 Simplifying x + -0.8 = 2.289104628 Reorder the terms: -0.8 + x = 2.289104628 Solving -0.8 + x = 2.289104628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.289104628 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.289104628 + 0.8 x = 2.289104628 + 0.8 Combine like terms: 2.289104628 + 0.8 = 3.089104628 x = 3.089104628 Simplifying x = 3.089104628Subproblem 2
x + -0.8 = -2.289104628 Simplifying x + -0.8 = -2.289104628 Reorder the terms: -0.8 + x = -2.289104628 Solving -0.8 + x = -2.289104628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.289104628 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.289104628 + 0.8 x = -2.289104628 + 0.8 Combine like terms: -2.289104628 + 0.8 = -1.489104628 x = -1.489104628 Simplifying x = -1.489104628Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.089104628, -1.489104628}
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