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Simplifying -7x2 + 16x + -3 = 0 Reorder the terms: -3 + 16x + -7x2 = 0 Solving -3 + 16x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.4285714286 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -2.285714286x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -2.285714286x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -2.285714286x + x2 = 0 + -0.4285714286 -2.285714286x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -2.285714286x + x2 = -0.4285714286 The x term is -2.285714286x. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x + 1.306122449 + x2 = -0.4285714286 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = -0.4285714286 + 1.306122449 Combine like terms: -0.4285714286 + 1.306122449 = 0.8775510204 1.306122449 + -2.285714286x + x2 = 0.8775510204 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 0.8775510204 Calculate the square root of the right side: 0.936776932 Break this problem into two subproblems by setting (x + -1.142857143) equal to 0.936776932 and -0.936776932.Subproblem 1
x + -1.142857143 = 0.936776932 Simplifying x + -1.142857143 = 0.936776932 Reorder the terms: -1.142857143 + x = 0.936776932 Solving -1.142857143 + x = 0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 0.936776932 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 0.936776932 + 1.142857143 x = 0.936776932 + 1.142857143 Combine like terms: 0.936776932 + 1.142857143 = 2.079634075 x = 2.079634075 Simplifying x = 2.079634075Subproblem 2
x + -1.142857143 = -0.936776932 Simplifying x + -1.142857143 = -0.936776932 Reorder the terms: -1.142857143 + x = -0.936776932 Solving -1.142857143 + x = -0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -0.936776932 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -0.936776932 + 1.142857143 x = -0.936776932 + 1.142857143 Combine like terms: -0.936776932 + 1.142857143 = 0.206080211 x = 0.206080211 Simplifying x = 0.206080211Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.079634075, 0.206080211}
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