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Simplifying 2x(x + 3) = 6 + -1x Reorder the terms: 2x(3 + x) = 6 + -1x (3 * 2x + x * 2x) = 6 + -1x (6x + 2x2) = 6 + -1x Solving 6x + 2x2 = 6 + -1x Solving for variable 'x'. Reorder the terms: -6 + 6x + x + 2x2 = 6 + -1x + -6 + x Combine like terms: 6x + x = 7x -6 + 7x + 2x2 = 6 + -1x + -6 + x Reorder the terms: -6 + 7x + 2x2 = 6 + -6 + -1x + x Combine like terms: 6 + -6 = 0 -6 + 7x + 2x2 = 0 + -1x + x -6 + 7x + 2x2 = -1x + x Combine like terms: -1x + x = 0 -6 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 3.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.5x + x2 = 0 + 3 3.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.5x + x2 = 3 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 = 3 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + 3.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 1.75 = 2.46221445 Simplifying x + 1.75 = 2.46221445 Reorder the terms: 1.75 + x = 2.46221445 Solving 1.75 + x = 2.46221445 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 = 2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.46221445 + -1.75 x = 2.46221445 + -1.75 Combine like terms: 2.46221445 + -1.75 = 0.71221445 x = 0.71221445 Simplifying x = 0.71221445Subproblem 2
x + 1.75 = -2.46221445 Simplifying x + 1.75 = -2.46221445 Reorder the terms: 1.75 + x = -2.46221445 Solving 1.75 + x = -2.46221445 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 = -2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.46221445 + -1.75 x = -2.46221445 + -1.75 Combine like terms: -2.46221445 + -1.75 = -4.21221445 x = -4.21221445 Simplifying x = -4.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71221445, -4.21221445}
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