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Simplifying 3x2 + -28 = -4x2 + -9x + -10 Reorder the terms: -28 + 3x2 = -4x2 + -9x + -10 Reorder the terms: -28 + 3x2 = -10 + -9x + -4x2 Solving -28 + 3x2 = -10 + -9x + -4x2 Solving for variable 'x'. Reorder the terms: -28 + 10 + 9x + 3x2 + 4x2 = -10 + -9x + -4x2 + 10 + 9x + 4x2 Combine like terms: -28 + 10 = -18 -18 + 9x + 3x2 + 4x2 = -10 + -9x + -4x2 + 10 + 9x + 4x2 Combine like terms: 3x2 + 4x2 = 7x2 -18 + 9x + 7x2 = -10 + -9x + -4x2 + 10 + 9x + 4x2 Reorder the terms: -18 + 9x + 7x2 = -10 + 10 + -9x + 9x + -4x2 + 4x2 Combine like terms: -10 + 10 = 0 -18 + 9x + 7x2 = 0 + -9x + 9x + -4x2 + 4x2 -18 + 9x + 7x2 = -9x + 9x + -4x2 + 4x2 Combine like terms: -9x + 9x = 0 -18 + 9x + 7x2 = 0 + -4x2 + 4x2 -18 + 9x + 7x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 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 = 1.084769517 x = 1.084769517 Simplifying x = 1.084769517Subproblem 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 = -2.370483803 x = -2.370483803 Simplifying x = -2.370483803Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.084769517, -2.370483803}
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