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Simplifying x(x + -3) = x + 5x + 7 Reorder the terms: x(-3 + x) = x + 5x + 7 (-3 * x + x * x) = x + 5x + 7 (-3x + x2) = x + 5x + 7 Reorder the terms: -3x + x2 = 7 + x + 5x Combine like terms: x + 5x = 6x -3x + x2 = 7 + 6x Solving -3x + x2 = 7 + 6x Solving for variable 'x'. Reorder the terms: -7 + -3x + -6x + x2 = 7 + 6x + -7 + -6x Combine like terms: -3x + -6x = -9x -7 + -9x + x2 = 7 + 6x + -7 + -6x Reorder the terms: -7 + -9x + x2 = 7 + -7 + 6x + -6x Combine like terms: 7 + -7 = 0 -7 + -9x + x2 = 0 + 6x + -6x -7 + -9x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -7 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -9x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -9x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9x + x2 = 0 + 7 -9x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9x + x2 = 7 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 7 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + -9x + x2 = 27.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -4.5 = 5.220153254 Simplifying x + -4.5 = 5.220153254 Reorder the terms: -4.5 + x = 5.220153254 Solving -4.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.220153254 + 4.5 x = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 x = 9.720153254 Simplifying x = 9.720153254Subproblem 2
x + -4.5 = -5.220153254 Simplifying x + -4.5 = -5.220153254 Reorder the terms: -4.5 + x = -5.220153254 Solving -4.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.220153254 + 4.5 x = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 x = -0.720153254 Simplifying x = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.720153254, -0.720153254}
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