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Simplifying x(2x + 8x + -3) = 9 + 7 * 2 Reorder the terms: x(-3 + 2x + 8x) = 9 + 7 * 2 Combine like terms: 2x + 8x = 10x x(-3 + 10x) = 9 + 7 * 2 (-3 * x + 10x * x) = 9 + 7 * 2 (-3x + 10x2) = 9 + 7 * 2 Multiply 7 * 2 -3x + 10x2 = 9 + 14 Combine like terms: 9 + 14 = 23 -3x + 10x2 = 23 Solving -3x + 10x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -3x + 10x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.3 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + -0.3x + 2.3 + x2 = 0.0 + 2.3 Reorder the terms: -2.3 + 2.3 + -0.3x + x2 = 0.0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + -0.3x + x2 = 0.0 + 2.3 -0.3x + x2 = 0.0 + 2.3 Combine like terms: 0.0 + 2.3 = 2.3 -0.3x + x2 = 2.3 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 2.3 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 2.3 + 0.0225 Combine like terms: 2.3 + 0.0225 = 2.3225 0.0225 + -0.3x + x2 = 2.3225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 2.3225 Calculate the square root of the right side: 1.523975065 Break this problem into two subproblems by setting (x + -0.15) equal to 1.523975065 and -1.523975065.Subproblem 1
x + -0.15 = 1.523975065 Simplifying x + -0.15 = 1.523975065 Reorder the terms: -0.15 + x = 1.523975065 Solving -0.15 + x = 1.523975065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.523975065 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.523975065 + 0.15 x = 1.523975065 + 0.15 Combine like terms: 1.523975065 + 0.15 = 1.673975065 x = 1.673975065 Simplifying x = 1.673975065Subproblem 2
x + -0.15 = -1.523975065 Simplifying x + -0.15 = -1.523975065 Reorder the terms: -0.15 + x = -1.523975065 Solving -0.15 + x = -1.523975065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.523975065 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.523975065 + 0.15 x = -1.523975065 + 0.15 Combine like terms: -1.523975065 + 0.15 = -1.373975065 x = -1.373975065 Simplifying x = -1.373975065Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.673975065, -1.373975065}
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