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Simplifying x(2x + -7) = 6(2x + 3) Reorder the terms: x(-7 + 2x) = 6(2x + 3) (-7 * x + 2x * x) = 6(2x + 3) (-7x + 2x2) = 6(2x + 3) Reorder the terms: -7x + 2x2 = 6(3 + 2x) -7x + 2x2 = (3 * 6 + 2x * 6) -7x + 2x2 = (18 + 12x) Solving -7x + 2x2 = 18 + 12x Solving for variable 'x'. Reorder the terms: -18 + -7x + -12x + 2x2 = 18 + 12x + -18 + -12x Combine like terms: -7x + -12x = -19x -18 + -19x + 2x2 = 18 + 12x + -18 + -12x Reorder the terms: -18 + -19x + 2x2 = 18 + -18 + 12x + -12x Combine like terms: 18 + -18 = 0 -18 + -19x + 2x2 = 0 + 12x + -12x -18 + -19x + 2x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -18 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -9.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -9.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -9.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9.5x + x2 = 0 + 9 -9.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9.5x + x2 = 9 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 9 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 9 + 22.5625 Combine like terms: 9 + 22.5625 = 31.5625 22.5625 + -9.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + -4.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + -4.75 = 5.618051264 Simplifying x + -4.75 = 5.618051264 Reorder the terms: -4.75 + x = 5.618051264 Solving -4.75 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.618051264 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.618051264 + 4.75 x = 5.618051264 + 4.75 Combine like terms: 5.618051264 + 4.75 = 10.368051264 x = 10.368051264 Simplifying x = 10.368051264Subproblem 2
x + -4.75 = -5.618051264 Simplifying x + -4.75 = -5.618051264 Reorder the terms: -4.75 + x = -5.618051264 Solving -4.75 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.618051264 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.618051264 + 4.75 x = -5.618051264 + 4.75 Combine like terms: -5.618051264 + 4.75 = -0.868051264 x = -0.868051264 Simplifying x = -0.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.368051264, -0.868051264}
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