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Simplifying 5x2 + -4x + -23 = 0 Reorder the terms: -23 + -4x + 5x2 = 0 Solving -23 + -4x + 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 + -0.8x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -0.8x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -0.8x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -0.8x + x2 = 0 + 4.6 -0.8x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -0.8x + x2 = 4.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 4.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 4.6 + 0.16 Combine like terms: 4.6 + 0.16 = 4.76 0.16 + -0.8x + x2 = 4.76 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 4.76 Calculate the square root of the right side: 2.181742423 Break this problem into two subproblems by setting (x + -0.4) equal to 2.181742423 and -2.181742423.Subproblem 1
x + -0.4 = 2.181742423 Simplifying x + -0.4 = 2.181742423 Reorder the terms: -0.4 + x = 2.181742423 Solving -0.4 + x = 2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 2.181742423 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 2.181742423 + 0.4 x = 2.181742423 + 0.4 Combine like terms: 2.181742423 + 0.4 = 2.581742423 x = 2.581742423 Simplifying x = 2.581742423Subproblem 2
x + -0.4 = -2.181742423 Simplifying x + -0.4 = -2.181742423 Reorder the terms: -0.4 + x = -2.181742423 Solving -0.4 + x = -2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -2.181742423 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -2.181742423 + 0.4 x = -2.181742423 + 0.4 Combine like terms: -2.181742423 + 0.4 = -1.781742423 x = -1.781742423 Simplifying x = -1.781742423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.581742423, -1.781742423}
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