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Simplifying 5x2 + -43x + -10 = 0 Reorder the terms: -10 + -43x + 5x2 = 0 Solving -10 + -43x + 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'. -2 + -8.6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -8.6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -8.6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8.6x + x2 = 0 + 2 -8.6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8.6x + x2 = 2 The x term is -8.6x. Take half its coefficient (-4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. -8.6x + 18.49 + x2 = 2 + 18.49 Reorder the terms: 18.49 + -8.6x + x2 = 2 + 18.49 Combine like terms: 2 + 18.49 = 20.49 18.49 + -8.6x + x2 = 20.49 Factor a perfect square on the left side: (x + -4.3)(x + -4.3) = 20.49 Calculate the square root of the right side: 4.526588119 Break this problem into two subproblems by setting (x + -4.3) equal to 4.526588119 and -4.526588119.Subproblem 1
x + -4.3 = 4.526588119 Simplifying x + -4.3 = 4.526588119 Reorder the terms: -4.3 + x = 4.526588119 Solving -4.3 + x = 4.526588119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + x = 4.526588119 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + x = 4.526588119 + 4.3 x = 4.526588119 + 4.3 Combine like terms: 4.526588119 + 4.3 = 8.826588119 x = 8.826588119 Simplifying x = 8.826588119Subproblem 2
x + -4.3 = -4.526588119 Simplifying x + -4.3 = -4.526588119 Reorder the terms: -4.3 + x = -4.526588119 Solving -4.3 + x = -4.526588119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + x = -4.526588119 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + x = -4.526588119 + 4.3 x = -4.526588119 + 4.3 Combine like terms: -4.526588119 + 4.3 = -0.226588119 x = -0.226588119 Simplifying x = -0.226588119Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.826588119, -0.226588119}
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