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Simplifying -2x(x + 3) = 3(x + -7) Reorder the terms: -2x(3 + x) = 3(x + -7) (3 * -2x + x * -2x) = 3(x + -7) (-6x + -2x2) = 3(x + -7) Reorder the terms: -6x + -2x2 = 3(-7 + x) -6x + -2x2 = (-7 * 3 + x * 3) -6x + -2x2 = (-21 + 3x) Solving -6x + -2x2 = -21 + 3x Solving for variable 'x'. Reorder the terms: 21 + -6x + -3x + -2x2 = -21 + 3x + 21 + -3x Combine like terms: -6x + -3x = -9x 21 + -9x + -2x2 = -21 + 3x + 21 + -3x Reorder the terms: 21 + -9x + -2x2 = -21 + 21 + 3x + -3x Combine like terms: -21 + 21 = 0 21 + -9x + -2x2 = 0 + 3x + -3x 21 + -9x + -2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 21 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -10.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 4.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 4.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 4.5x + x2 = 0 + 10.5 4.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 4.5x + x2 = 10.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 10.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 10.5 + 5.0625 Combine like terms: 10.5 + 5.0625 = 15.5625 5.0625 + 4.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 2.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 2.25 = 3.94493346 Simplifying x + 2.25 = 3.94493346 Reorder the terms: 2.25 + x = 3.94493346 Solving 2.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.94493346 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.94493346 + -2.25 x = 3.94493346 + -2.25 Combine like terms: 3.94493346 + -2.25 = 1.69493346 x = 1.69493346 Simplifying x = 1.69493346Subproblem 2
x + 2.25 = -3.94493346 Simplifying x + 2.25 = -3.94493346 Reorder the terms: 2.25 + x = -3.94493346 Solving 2.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.94493346 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.94493346 + -2.25 x = -3.94493346 + -2.25 Combine like terms: -3.94493346 + -2.25 = -6.19493346 x = -6.19493346 Simplifying x = -6.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.69493346, -6.19493346}
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