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Simplifying 4x(x + -3) = 29 Reorder the terms: 4x(-3 + x) = 29 (-3 * 4x + x * 4x) = 29 (-12x + 4x2) = 29 Solving -12x + 4x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + -12x + 4x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -3x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -3x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -3x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -3x + x2 = 0 + 7.25 -3x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -3x + x2 = 7.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 7.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 7.25 + 2.25 Combine like terms: 7.25 + 2.25 = 9.5 2.25 + -3x + x2 = 9.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -1.5) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -1.5 = 3.082207001 Simplifying x + -1.5 = 3.082207001 Reorder the terms: -1.5 + x = 3.082207001 Solving -1.5 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.082207001 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.082207001 + 1.5 x = 3.082207001 + 1.5 Combine like terms: 3.082207001 + 1.5 = 4.582207001 x = 4.582207001 Simplifying x = 4.582207001Subproblem 2
x + -1.5 = -3.082207001 Simplifying x + -1.5 = -3.082207001 Reorder the terms: -1.5 + x = -3.082207001 Solving -1.5 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.082207001 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.082207001 + 1.5 x = -3.082207001 + 1.5 Combine like terms: -3.082207001 + 1.5 = -1.582207001 x = -1.582207001 Simplifying x = -1.582207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.582207001, -1.582207001}
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