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Simplifying 2x(x + 3) + -7 = 5(5 + -1x) + (x + 1) Reorder the terms: 2x(3 + x) + -7 = 5(5 + -1x) + (x + 1) (3 * 2x + x * 2x) + -7 = 5(5 + -1x) + (x + 1) (6x + 2x2) + -7 = 5(5 + -1x) + (x + 1) Reorder the terms: -7 + 6x + 2x2 = 5(5 + -1x) + (x + 1) -7 + 6x + 2x2 = (5 * 5 + -1x * 5) + (x + 1) -7 + 6x + 2x2 = (25 + -5x) + (x + 1) Reorder the terms: -7 + 6x + 2x2 = 25 + -5x + (1 + x) Remove parenthesis around (1 + x) -7 + 6x + 2x2 = 25 + -5x + 1 + x Reorder the terms: -7 + 6x + 2x2 = 25 + 1 + -5x + x Combine like terms: 25 + 1 = 26 -7 + 6x + 2x2 = 26 + -5x + x Combine like terms: -5x + x = -4x -7 + 6x + 2x2 = 26 + -4x Solving -7 + 6x + 2x2 = 26 + -4x Solving for variable 'x'. Reorder the terms: -7 + -26 + 6x + 4x + 2x2 = 26 + -4x + -26 + 4x Combine like terms: -7 + -26 = -33 -33 + 6x + 4x + 2x2 = 26 + -4x + -26 + 4x Combine like terms: 6x + 4x = 10x -33 + 10x + 2x2 = 26 + -4x + -26 + 4x Reorder the terms: -33 + 10x + 2x2 = 26 + -26 + -4x + 4x Combine like terms: 26 + -26 = 0 -33 + 10x + 2x2 = 0 + -4x + 4x -33 + 10x + 2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -33 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 5x + x2 = 0 + 16.5 5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 5x + x2 = 16.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 16.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 16.5 + 6.25 Combine like terms: 16.5 + 6.25 = 22.75 6.25 + 5x + x2 = 22.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + 2.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + 2.5 = 4.769696007 Simplifying x + 2.5 = 4.769696007 Reorder the terms: 2.5 + x = 4.769696007 Solving 2.5 + x = 4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.769696007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.769696007 + -2.5 x = 4.769696007 + -2.5 Combine like terms: 4.769696007 + -2.5 = 2.269696007 x = 2.269696007 Simplifying x = 2.269696007Subproblem 2
x + 2.5 = -4.769696007 Simplifying x + 2.5 = -4.769696007 Reorder the terms: 2.5 + x = -4.769696007 Solving 2.5 + x = -4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.769696007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.769696007 + -2.5 x = -4.769696007 + -2.5 Combine like terms: -4.769696007 + -2.5 = -7.269696007 x = -7.269696007 Simplifying x = -7.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.269696007, -7.269696007}
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