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Simplifying 2x2 + -7x + 9 = (x + 3)(x + 1) + 3x Reorder the terms: 9 + -7x + 2x2 = (x + 3)(x + 1) + 3x Reorder the terms: 9 + -7x + 2x2 = (3 + x)(x + 1) + 3x Reorder the terms: 9 + -7x + 2x2 = (3 + x)(1 + x) + 3x Multiply (3 + x) * (1 + x) 9 + -7x + 2x2 = (3(1 + x) + x(1 + x)) + 3x 9 + -7x + 2x2 = ((1 * 3 + x * 3) + x(1 + x)) + 3x 9 + -7x + 2x2 = ((3 + 3x) + x(1 + x)) + 3x 9 + -7x + 2x2 = (3 + 3x + (1 * x + x * x)) + 3x 9 + -7x + 2x2 = (3 + 3x + (1x + x2)) + 3x Combine like terms: 3x + 1x = 4x 9 + -7x + 2x2 = (3 + 4x + x2) + 3x Reorder the terms: 9 + -7x + 2x2 = 3 + 4x + 3x + x2 Combine like terms: 4x + 3x = 7x 9 + -7x + 2x2 = 3 + 7x + x2 Solving 9 + -7x + 2x2 = 3 + 7x + x2 Solving for variable 'x'. Reorder the terms: 9 + -3 + -7x + -7x + 2x2 + -1x2 = 3 + 7x + x2 + -3 + -7x + -1x2 Combine like terms: 9 + -3 = 6 6 + -7x + -7x + 2x2 + -1x2 = 3 + 7x + x2 + -3 + -7x + -1x2 Combine like terms: -7x + -7x = -14x 6 + -14x + 2x2 + -1x2 = 3 + 7x + x2 + -3 + -7x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 6 + -14x + 1x2 = 3 + 7x + x2 + -3 + -7x + -1x2 Reorder the terms: 6 + -14x + 1x2 = 3 + -3 + 7x + -7x + x2 + -1x2 Combine like terms: 3 + -3 = 0 6 + -14x + 1x2 = 0 + 7x + -7x + x2 + -1x2 6 + -14x + 1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 6 + -14x + 1x2 = 0 + x2 + -1x2 6 + -14x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6 + -14x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -14x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -14x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -14x + x2 = 0 + -6 -14x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -14x + x2 = -6 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -6 + 49 Reorder the terms: 49 + -14x + x2 = -6 + 49 Combine like terms: -6 + 49 = 43 49 + -14x + x2 = 43 Factor a perfect square on the left side: (x + -7)(x + -7) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -7) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -7 = 6.557438524 Simplifying x + -7 = 6.557438524 Reorder the terms: -7 + x = 6.557438524 Solving -7 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.557438524 + 7 x = 6.557438524 + 7 Combine like terms: 6.557438524 + 7 = 13.557438524 x = 13.557438524 Simplifying x = 13.557438524Subproblem 2
x + -7 = -6.557438524 Simplifying x + -7 = -6.557438524 Reorder the terms: -7 + x = -6.557438524 Solving -7 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.557438524 + 7 x = -6.557438524 + 7 Combine like terms: -6.557438524 + 7 = 0.442561476 x = 0.442561476 Simplifying x = 0.442561476Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.557438524, 0.442561476}
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