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Simplifying 3(x + -4) + -7 = -2x(x + -5) Reorder the terms: 3(-4 + x) + -7 = -2x(x + -5) (-4 * 3 + x * 3) + -7 = -2x(x + -5) (-12 + 3x) + -7 = -2x(x + -5) Reorder the terms: -12 + -7 + 3x = -2x(x + -5) Combine like terms: -12 + -7 = -19 -19 + 3x = -2x(x + -5) Reorder the terms: -19 + 3x = -2x(-5 + x) -19 + 3x = (-5 * -2x + x * -2x) -19 + 3x = (10x + -2x2) Solving -19 + 3x = 10x + -2x2 Solving for variable 'x'. Combine like terms: 3x + -10x = -7x -19 + -7x + 2x2 = 10x + -2x2 + -10x + 2x2 Reorder the terms: -19 + -7x + 2x2 = 10x + -10x + -2x2 + 2x2 Combine like terms: 10x + -10x = 0 -19 + -7x + 2x2 = 0 + -2x2 + 2x2 -19 + -7x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -19 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -3.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -3.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -3.5x + x2 = 0 + 9.5 -3.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -3.5x + x2 = 9.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 9.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + -3.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -1.75 = 3.54436172 Simplifying x + -1.75 = 3.54436172 Reorder the terms: -1.75 + x = 3.54436172 Solving -1.75 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.54436172 + 1.75 x = 3.54436172 + 1.75 Combine like terms: 3.54436172 + 1.75 = 5.29436172 x = 5.29436172 Simplifying x = 5.29436172Subproblem 2
x + -1.75 = -3.54436172 Simplifying x + -1.75 = -3.54436172 Reorder the terms: -1.75 + x = -3.54436172 Solving -1.75 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.54436172 + 1.75 x = -3.54436172 + 1.75 Combine like terms: -3.54436172 + 1.75 = -1.79436172 x = -1.79436172 Simplifying x = -1.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.29436172, -1.79436172}
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