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Simplifying 5x2 + 20x + -588 = 0 Reorder the terms: -588 + 20x + 5x2 = 0 Solving -588 + 20x + 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'. -117.6 + 4x + x2 = 0 Move the constant term to the right: Add '117.6' to each side of the equation. -117.6 + 4x + 117.6 + x2 = 0 + 117.6 Reorder the terms: -117.6 + 117.6 + 4x + x2 = 0 + 117.6 Combine like terms: -117.6 + 117.6 = 0.0 0.0 + 4x + x2 = 0 + 117.6 4x + x2 = 0 + 117.6 Combine like terms: 0 + 117.6 = 117.6 4x + x2 = 117.6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 117.6 + 4 Reorder the terms: 4 + 4x + x2 = 117.6 + 4 Combine like terms: 117.6 + 4 = 121.6 4 + 4x + x2 = 121.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 121.6 Calculate the square root of the right side: 11.027239002 Break this problem into two subproblems by setting (x + 2) equal to 11.027239002 and -11.027239002.Subproblem 1
x + 2 = 11.027239002 Simplifying x + 2 = 11.027239002 Reorder the terms: 2 + x = 11.027239002 Solving 2 + x = 11.027239002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.027239002 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.027239002 + -2 x = 11.027239002 + -2 Combine like terms: 11.027239002 + -2 = 9.027239002 x = 9.027239002 Simplifying x = 9.027239002Subproblem 2
x + 2 = -11.027239002 Simplifying x + 2 = -11.027239002 Reorder the terms: 2 + x = -11.027239002 Solving 2 + x = -11.027239002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.027239002 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.027239002 + -2 x = -11.027239002 + -2 Combine like terms: -11.027239002 + -2 = -13.027239002 x = -13.027239002 Simplifying x = -13.027239002Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.027239002, -13.027239002}
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