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Simplifying 7x2 + -9x + -10 = 8 Reorder the terms: -10 + -9x + 7x2 = 8 Solving -10 + -9x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -10 + -8 + -9x + 7x2 = 8 + -8 Combine like terms: -10 + -8 = -18 -18 + -9x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -18 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -1.285714286x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -1.285714286x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 2.571428571 -1.285714286x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -1.285714286x + x2 = 2.571428571 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 = 2.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 2.571428571 + 0.4132653063 Combine like terms: 2.571428571 + 0.4132653063 = 2.9846938773 0.4132653063 + -1.285714286x + x2 = 2.9846938773 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 2.9846938773 Calculate the square root of the right side: 1.72762666 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.72762666 and -1.72762666.Subproblem 1
x + -0.642857143 = 1.72762666 Simplifying x + -0.642857143 = 1.72762666 Reorder the terms: -0.642857143 + x = 1.72762666 Solving -0.642857143 + x = 1.72762666 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 = 1.72762666 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.72762666 + 0.642857143 x = 1.72762666 + 0.642857143 Combine like terms: 1.72762666 + 0.642857143 = 2.370483803 x = 2.370483803 Simplifying x = 2.370483803Subproblem 2
x + -0.642857143 = -1.72762666 Simplifying x + -0.642857143 = -1.72762666 Reorder the terms: -0.642857143 + x = -1.72762666 Solving -0.642857143 + x = -1.72762666 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 = -1.72762666 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.72762666 + 0.642857143 x = -1.72762666 + 0.642857143 Combine like terms: -1.72762666 + 0.642857143 = -1.084769517 x = -1.084769517 Simplifying x = -1.084769517Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.370483803, -1.084769517}
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