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Simplifying 9x + 7x2 = 63 Solving 9x + 7x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 9x + 7x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.285714286x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 1.285714286x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.285714286x + x2 = 0 + 9 1.285714286x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.285714286x + x2 = 9 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 = 9 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 9 + 0.4132653063 Combine like terms: 9 + 0.4132653063 = 9.4132653063 0.4132653063 + 1.285714286x + x2 = 9.4132653063 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 9.4132653063 Calculate the square root of the right side: 3.068104514 Break this problem into two subproblems by setting (x + 0.642857143) equal to 3.068104514 and -3.068104514.Subproblem 1
x + 0.642857143 = 3.068104514 Simplifying x + 0.642857143 = 3.068104514 Reorder the terms: 0.642857143 + x = 3.068104514 Solving 0.642857143 + x = 3.068104514 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 = 3.068104514 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 3.068104514 + -0.642857143 x = 3.068104514 + -0.642857143 Combine like terms: 3.068104514 + -0.642857143 = 2.425247371 x = 2.425247371 Simplifying x = 2.425247371Subproblem 2
x + 0.642857143 = -3.068104514 Simplifying x + 0.642857143 = -3.068104514 Reorder the terms: 0.642857143 + x = -3.068104514 Solving 0.642857143 + x = -3.068104514 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 = -3.068104514 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -3.068104514 + -0.642857143 x = -3.068104514 + -0.642857143 Combine like terms: -3.068104514 + -0.642857143 = -3.710961657 x = -3.710961657 Simplifying x = -3.710961657Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.425247371, -3.710961657}
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