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Simplifying (5x2) + 4x + -56 = 0 Reorder the terms: -56 + 4x + (5x2) = 0 Solving -56 + 4x + (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'. -11.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + 0.8x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + 0.8x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + 0.8x + x2 = 0 + 11.2 0.8x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 0.8x + x2 = 11.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 11.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 11.2 + 0.16 Combine like terms: 11.2 + 0.16 = 11.36 0.16 + 0.8x + x2 = 11.36 Factor a perfect square on the left side: ((x) + 0.4)((x) + 0.4) = 11.36 Calculate the square root of the right side: 3.370459909 Break this problem into two subproblems by setting ((x) + 0.4) equal to 3.370459909 and -3.370459909.Subproblem 1
(x) + 0.4 = 3.370459909 Simplifying (x) + 0.4 = 3.370459909 x + 0.4 = 3.370459909 Reorder the terms: 0.4 + x = 3.370459909 Solving 0.4 + x = 3.370459909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 3.370459909 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 3.370459909 + -0.4 x = 3.370459909 + -0.4 Combine like terms: 3.370459909 + -0.4 = 2.970459909 x = 2.970459909 Simplifying x = 2.970459909Subproblem 2
(x) + 0.4 = -3.370459909 Simplifying (x) + 0.4 = -3.370459909 x + 0.4 = -3.370459909 Reorder the terms: 0.4 + x = -3.370459909 Solving 0.4 + x = -3.370459909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -3.370459909 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -3.370459909 + -0.4 x = -3.370459909 + -0.4 Combine like terms: -3.370459909 + -0.4 = -3.770459909 x = -3.770459909 Simplifying x = -3.770459909Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.970459909, -3.770459909}
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