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Simplifying 7x2 + 9x = 8 Reorder the terms: 9x + 7x2 = 8 Solving 9x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 9x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 1.285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 1.285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 1.285714286x + x2 = 0 + 1.142857143 1.285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 1.285714286x + x2 = 1.142857143 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 = 1.142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 1.142857143 + 0.4132653063 Combine like terms: 1.142857143 + 0.4132653063 = 1.5561224493 0.4132653063 + 1.285714286x + x2 = 1.5561224493 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 1.5561224493 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (x + 0.642857143) equal to 1.247446371 and -1.247446371.Subproblem 1
x + 0.642857143 = 1.247446371 Simplifying x + 0.642857143 = 1.247446371 Reorder the terms: 0.642857143 + x = 1.247446371 Solving 0.642857143 + x = 1.247446371 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 = 1.247446371 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 1.247446371 + -0.642857143 x = 1.247446371 + -0.642857143 Combine like terms: 1.247446371 + -0.642857143 = 0.604589228 x = 0.604589228 Simplifying x = 0.604589228Subproblem 2
x + 0.642857143 = -1.247446371 Simplifying x + 0.642857143 = -1.247446371 Reorder the terms: 0.642857143 + x = -1.247446371 Solving 0.642857143 + x = -1.247446371 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 = -1.247446371 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -1.247446371 + -0.642857143 x = -1.247446371 + -0.642857143 Combine like terms: -1.247446371 + -0.642857143 = -1.890303514 x = -1.890303514 Simplifying x = -1.890303514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.604589228, -1.890303514}
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