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Simplifying 3 + -7x2 + 9x = 0 Reorder the terms: 3 + 9x + -7x2 = 0 Solving 3 + 9x + -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 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.285714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.285714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.285714286x + x2 = 0 + 0.4285714286 -1.285714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.285714286x + x2 = 0.4285714286 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 0.4285714286 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 0.4285714286 + 0.4132653063 Combine like terms: 0.4285714286 + 0.4132653063 = 0.8418367349 0.4132653063 + -1.285714286x + x2 = 0.8418367349 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 0.8418367349 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (x + -0.642857143) equal to 0.917516613 and -0.917516613.Subproblem 1
x + -0.642857143 = 0.917516613 Simplifying x + -0.642857143 = 0.917516613 Reorder the terms: -0.642857143 + x = 0.917516613 Solving -0.642857143 + x = 0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 0.917516613 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 0.917516613 + 0.642857143 x = 0.917516613 + 0.642857143 Combine like terms: 0.917516613 + 0.642857143 = 1.560373756 x = 1.560373756 Simplifying x = 1.560373756Subproblem 2
x + -0.642857143 = -0.917516613 Simplifying x + -0.642857143 = -0.917516613 Reorder the terms: -0.642857143 + x = -0.917516613 Solving -0.642857143 + x = -0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -0.917516613 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -0.917516613 + 0.642857143 x = -0.917516613 + 0.642857143 Combine like terms: -0.917516613 + 0.642857143 = -0.27465947 x = -0.27465947 Simplifying x = -0.27465947Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560373756, -0.27465947}
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