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Simplifying 5x2 + 28x + -10 = 0 Reorder the terms: -10 + 28x + 5x2 = 0 Solving -10 + 28x + 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 + 5.6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 5.6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 5.6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5.6x + x2 = 0 + 2 5.6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 5.6x + x2 = 2 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = 2 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 2 + 7.84 Combine like terms: 2 + 7.84 = 9.84 7.84 + 5.6x + x2 = 9.84 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 9.84 Calculate the square root of the right side: 3.136877428 Break this problem into two subproblems by setting (x + 2.8) equal to 3.136877428 and -3.136877428.Subproblem 1
x + 2.8 = 3.136877428 Simplifying x + 2.8 = 3.136877428 Reorder the terms: 2.8 + x = 3.136877428 Solving 2.8 + x = 3.136877428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 3.136877428 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 3.136877428 + -2.8 x = 3.136877428 + -2.8 Combine like terms: 3.136877428 + -2.8 = 0.336877428 x = 0.336877428 Simplifying x = 0.336877428Subproblem 2
x + 2.8 = -3.136877428 Simplifying x + 2.8 = -3.136877428 Reorder the terms: 2.8 + x = -3.136877428 Solving 2.8 + x = -3.136877428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -3.136877428 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -3.136877428 + -2.8 x = -3.136877428 + -2.8 Combine like terms: -3.136877428 + -2.8 = -5.936877428 x = -5.936877428 Simplifying x = -5.936877428Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.336877428, -5.936877428}
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