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Simplifying (-3x2 + 2x + -7) + (5x2 + 6x + 1) = 0 Reorder the terms: (-7 + 2x + -3x2) + (5x2 + 6x + 1) = 0 Remove parenthesis around (-7 + 2x + -3x2) -7 + 2x + -3x2 + (5x2 + 6x + 1) = 0 Reorder the terms: -7 + 2x + -3x2 + (1 + 6x + 5x2) = 0 Remove parenthesis around (1 + 6x + 5x2) -7 + 2x + -3x2 + 1 + 6x + 5x2 = 0 Reorder the terms: -7 + 1 + 2x + 6x + -3x2 + 5x2 = 0 Combine like terms: -7 + 1 = -6 -6 + 2x + 6x + -3x2 + 5x2 = 0 Combine like terms: 2x + 6x = 8x -6 + 8x + -3x2 + 5x2 = 0 Combine like terms: -3x2 + 5x2 = 2x2 -6 + 8x + 2x2 = 0 Solving -6 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4x + x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + x2 = 0 Solving -3 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311Subproblem 2
x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}Solution
x = {0.645751311, -4.645751311}
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