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Simplifying 4x(x + -3) + 5x = 48 Reorder the terms: 4x(-3 + x) + 5x = 48 (-3 * 4x + x * 4x) + 5x = 48 (-12x + 4x2) + 5x = 48 Reorder the terms: -12x + 5x + 4x2 = 48 Combine like terms: -12x + 5x = -7x -7x + 4x2 = 48 Solving -7x + 4x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -7x + 4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12 + -1.75x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.75x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -1.75x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.75x + x2 = 0 + 12 -1.75x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.75x + x2 = 12 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 12 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 12 + 0.765625 Combine like terms: 12 + 0.765625 = 12.765625 0.765625 + -1.75x + x2 = 12.765625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 12.765625 Calculate the square root of the right side: 3.572901482 Break this problem into two subproblems by setting (x + -0.875) equal to 3.572901482 and -3.572901482.Subproblem 1
x + -0.875 = 3.572901482 Simplifying x + -0.875 = 3.572901482 Reorder the terms: -0.875 + x = 3.572901482 Solving -0.875 + x = 3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 3.572901482 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 3.572901482 + 0.875 x = 3.572901482 + 0.875 Combine like terms: 3.572901482 + 0.875 = 4.447901482 x = 4.447901482 Simplifying x = 4.447901482Subproblem 2
x + -0.875 = -3.572901482 Simplifying x + -0.875 = -3.572901482 Reorder the terms: -0.875 + x = -3.572901482 Solving -0.875 + x = -3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -3.572901482 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -3.572901482 + 0.875 x = -3.572901482 + 0.875 Combine like terms: -3.572901482 + 0.875 = -2.697901482 x = -2.697901482 Simplifying x = -2.697901482Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.447901482, -2.697901482}
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