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Simplifying 5x2 + 5x + -288 = 0 Reorder the terms: -288 + 5x + 5x2 = 0 Solving -288 + 5x + 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'. -57.6 + x + x2 = 0 Move the constant term to the right: Add '57.6' to each side of the equation. -57.6 + x + 57.6 + x2 = 0 + 57.6 Reorder the terms: -57.6 + 57.6 + x + x2 = 0 + 57.6 Combine like terms: -57.6 + 57.6 = 0.0 0.0 + x + x2 = 0 + 57.6 x + x2 = 0 + 57.6 Combine like terms: 0 + 57.6 = 57.6 x + x2 = 57.6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 57.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 57.6 + 0.25 Combine like terms: 57.6 + 0.25 = 57.85 1.25 + x2 = 57.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 57.85 Calculate the square root of the right side: 7.605918748 Break this problem into two subproblems by setting (x + 0.5) equal to 7.605918748 and -7.605918748.Subproblem 1
x + 0.5 = 7.605918748 Simplifying x + 0.5 = 7.605918748 Reorder the terms: 0.5 + x = 7.605918748 Solving 0.5 + x = 7.605918748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.605918748 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.605918748 + -0.5 x = 7.605918748 + -0.5 Combine like terms: 7.605918748 + -0.5 = 7.105918748 x = 7.105918748 Simplifying x = 7.105918748Subproblem 2
x + 0.5 = -7.605918748 Simplifying x + 0.5 = -7.605918748 Reorder the terms: 0.5 + x = -7.605918748 Solving 0.5 + x = -7.605918748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.605918748 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.605918748 + -0.5 x = -7.605918748 + -0.5 Combine like terms: -7.605918748 + -0.5 = -8.105918748 x = -8.105918748 Simplifying x = -8.105918748Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.105918748, -8.105918748}
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