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Simplifying 3x2 + 5x + -25 = 656 Reorder the terms: -25 + 5x + 3x2 = 656 Solving -25 + 5x + 3x2 = 656 Solving for variable 'x'. Reorder the terms: -25 + -656 + 5x + 3x2 = 656 + -656 Combine like terms: -25 + -656 = -681 -681 + 5x + 3x2 = 656 + -656 Combine like terms: 656 + -656 = 0 -681 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -227 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '227' to each side of the equation. -227 + 1.666666667x + 227 + x2 = 0 + 227 Reorder the terms: -227 + 227 + 1.666666667x + x2 = 0 + 227 Combine like terms: -227 + 227 = 0 0 + 1.666666667x + x2 = 0 + 227 1.666666667x + x2 = 0 + 227 Combine like terms: 0 + 227 = 227 1.666666667x + x2 = 227 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 227 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 227 + 0.6944444447 Combine like terms: 227 + 0.6944444447 = 227.6944444447 0.6944444447 + 1.666666667x + x2 = 227.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 227.6944444447 Calculate the square root of the right side: 15.089547523 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 15.089547523 and -15.089547523.Subproblem 1
x + 0.8333333335 = 15.089547523 Simplifying x + 0.8333333335 = 15.089547523 Reorder the terms: 0.8333333335 + x = 15.089547523 Solving 0.8333333335 + x = 15.089547523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 15.089547523 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 15.089547523 + -0.8333333335 x = 15.089547523 + -0.8333333335 Combine like terms: 15.089547523 + -0.8333333335 = 14.2562141895 x = 14.2562141895 Simplifying x = 14.2562141895Subproblem 2
x + 0.8333333335 = -15.089547523 Simplifying x + 0.8333333335 = -15.089547523 Reorder the terms: 0.8333333335 + x = -15.089547523 Solving 0.8333333335 + x = -15.089547523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -15.089547523 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -15.089547523 + -0.8333333335 x = -15.089547523 + -0.8333333335 Combine like terms: -15.089547523 + -0.8333333335 = -15.9228808565 x = -15.9228808565 Simplifying x = -15.9228808565Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.2562141895, -15.9228808565}
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