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Simplifying (0.2x + 8)(7x + -0.2) = 0 Reorder the terms: (8 + 0.2x)(7x + -0.2) = 0 Reorder the terms: (8 + 0.2x)(-0.2 + 7x) = 0 Multiply (8 + 0.2x) * (-0.2 + 7x) (8(-0.2 + 7x) + 0.2x * (-0.2 + 7x)) = 0 ((-0.2 * 8 + 7x * 8) + 0.2x * (-0.2 + 7x)) = 0 ((-1.6 + 56x) + 0.2x * (-0.2 + 7x)) = 0 (-1.6 + 56x + (-0.2 * 0.2x + 7x * 0.2x)) = 0 (-1.6 + 56x + (-0.04x + 1.4x2)) = 0 Combine like terms: 56x + -0.04x = 55.96x (-1.6 + 55.96x + 1.4x2) = 0 Solving -1.6 + 55.96x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -1.142857143 + 39.97142857x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 39.97142857x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 39.97142857x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 39.97142857x + x2 = 0 + 1.142857143 39.97142857x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 39.97142857x + x2 = 1.142857143 The x term is 39.97142857x. Take half its coefficient (19.98571429). Square it (399.4287757) and add it to both sides. Add '399.4287757' to each side of the equation. 39.97142857x + 399.4287757 + x2 = 1.142857143 + 399.4287757 Reorder the terms: 399.4287757 + 39.97142857x + x2 = 1.142857143 + 399.4287757 Combine like terms: 1.142857143 + 399.4287757 = 400.571632843 399.4287757 + 39.97142857x + x2 = 400.571632843 Factor a perfect square on the left side: (x + 19.98571429)(x + 19.98571429) = 400.571632843 Calculate the square root of the right side: 20.014285719 Break this problem into two subproblems by setting (x + 19.98571429) equal to 20.014285719 and -20.014285719.Subproblem 1
x + 19.98571429 = 20.014285719 Simplifying x + 19.98571429 = 20.014285719 Reorder the terms: 19.98571429 + x = 20.014285719 Solving 19.98571429 + x = 20.014285719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.98571429' to each side of the equation. 19.98571429 + -19.98571429 + x = 20.014285719 + -19.98571429 Combine like terms: 19.98571429 + -19.98571429 = 0.00000000 0.00000000 + x = 20.014285719 + -19.98571429 x = 20.014285719 + -19.98571429 Combine like terms: 20.014285719 + -19.98571429 = 0.028571429 x = 0.028571429 Simplifying x = 0.028571429Subproblem 2
x + 19.98571429 = -20.014285719 Simplifying x + 19.98571429 = -20.014285719 Reorder the terms: 19.98571429 + x = -20.014285719 Solving 19.98571429 + x = -20.014285719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.98571429' to each side of the equation. 19.98571429 + -19.98571429 + x = -20.014285719 + -19.98571429 Combine like terms: 19.98571429 + -19.98571429 = 0.00000000 0.00000000 + x = -20.014285719 + -19.98571429 x = -20.014285719 + -19.98571429 Combine like terms: -20.014285719 + -19.98571429 = -40.000000009 x = -40.000000009 Simplifying x = -40.000000009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.028571429, -40.000000009}
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