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Simplifying -7x2 + 9x + 12 = 0 Reorder the terms: 12 + 9x + -7x2 = 0 Solving 12 + 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'. -1.714285714 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1.285714286x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1.285714286x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 1.714285714 -1.285714286x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1.285714286x + x2 = 1.714285714 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 = 1.714285714 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1.714285714 + 0.4132653063 Combine like terms: 1.714285714 + 0.4132653063 = 2.1275510203 0.4132653063 + -1.285714286x + x2 = 2.1275510203 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 2.1275510203 Calculate the square root of the right side: 1.458612704 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.458612704 and -1.458612704.Subproblem 1
x + -0.642857143 = 1.458612704 Simplifying x + -0.642857143 = 1.458612704 Reorder the terms: -0.642857143 + x = 1.458612704 Solving -0.642857143 + x = 1.458612704 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 = 1.458612704 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.458612704 + 0.642857143 x = 1.458612704 + 0.642857143 Combine like terms: 1.458612704 + 0.642857143 = 2.101469847 x = 2.101469847 Simplifying x = 2.101469847Subproblem 2
x + -0.642857143 = -1.458612704 Simplifying x + -0.642857143 = -1.458612704 Reorder the terms: -0.642857143 + x = -1.458612704 Solving -0.642857143 + x = -1.458612704 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 = -1.458612704 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.458612704 + 0.642857143 x = -1.458612704 + 0.642857143 Combine like terms: -1.458612704 + 0.642857143 = -0.815755561 x = -0.815755561 Simplifying x = -0.815755561Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.101469847, -0.815755561}
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