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Simplifying -5x2 + -5x + 10 = -2x2 + -4x + 7 Reorder the terms: 10 + -5x + -5x2 = -2x2 + -4x + 7 Reorder the terms: 10 + -5x + -5x2 = 7 + -4x + -2x2 Solving 10 + -5x + -5x2 = 7 + -4x + -2x2 Solving for variable 'x'. Reorder the terms: 10 + -7 + -5x + 4x + -5x2 + 2x2 = 7 + -4x + -2x2 + -7 + 4x + 2x2 Combine like terms: 10 + -7 = 3 3 + -5x + 4x + -5x2 + 2x2 = 7 + -4x + -2x2 + -7 + 4x + 2x2 Combine like terms: -5x + 4x = -1x 3 + -1x + -5x2 + 2x2 = 7 + -4x + -2x2 + -7 + 4x + 2x2 Combine like terms: -5x2 + 2x2 = -3x2 3 + -1x + -3x2 = 7 + -4x + -2x2 + -7 + 4x + 2x2 Reorder the terms: 3 + -1x + -3x2 = 7 + -7 + -4x + 4x + -2x2 + 2x2 Combine like terms: 7 + -7 = 0 3 + -1x + -3x2 = 0 + -4x + 4x + -2x2 + 2x2 3 + -1x + -3x2 = -4x + 4x + -2x2 + 2x2 Combine like terms: -4x + 4x = 0 3 + -1x + -3x2 = 0 + -2x2 + 2x2 3 + -1x + -3x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 3 + -1x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.3333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3333333333x + x2 = 0 + 1 0.3333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.3333333333x + x2 = 1 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + 0.3333333333x + x2 = 1.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.013793755 and -1.013793755.Subproblem 1
x + 0.1666666667 = 1.013793755 Simplifying x + 0.1666666667 = 1.013793755 Reorder the terms: 0.1666666667 + x = 1.013793755 Solving 0.1666666667 + x = 1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.013793755 + -0.1666666667 x = 1.013793755 + -0.1666666667 Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883 x = 0.8471270883 Simplifying x = 0.8471270883Subproblem 2
x + 0.1666666667 = -1.013793755 Simplifying x + 0.1666666667 = -1.013793755 Reorder the terms: 0.1666666667 + x = -1.013793755 Solving 0.1666666667 + x = -1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.013793755 + -0.1666666667 x = -1.013793755 + -0.1666666667 Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217 x = -1.1804604217 Simplifying x = -1.1804604217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8471270883, -1.1804604217}
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