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Simplifying (-6x2 + 5x + -3) + (4x2 + x + 7) = 0 Reorder the terms: (-3 + 5x + -6x2) + (4x2 + x + 7) = 0 Remove parenthesis around (-3 + 5x + -6x2) -3 + 5x + -6x2 + (4x2 + x + 7) = 0 Reorder the terms: -3 + 5x + -6x2 + (7 + x + 4x2) = 0 Remove parenthesis around (7 + x + 4x2) -3 + 5x + -6x2 + 7 + x + 4x2 = 0 Reorder the terms: -3 + 7 + 5x + x + -6x2 + 4x2 = 0 Combine like terms: -3 + 7 = 4 4 + 5x + x + -6x2 + 4x2 = 0 Combine like terms: 5x + x = 6x 4 + 6x + -6x2 + 4x2 = 0 Combine like terms: -6x2 + 4x2 = -2x2 4 + 6x + -2x2 = 0 Solving 4 + 6x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + -1x2 = 0 Solving 2 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -3x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x + x2 = 0 + 2 -3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3x + x2 = 2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3x + x2 = 4.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -1.5 = 2.061552813 Simplifying x + -1.5 = 2.061552813 Reorder the terms: -1.5 + x = 2.061552813 Solving -1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.061552813 + 1.5 x = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 x = 3.561552813 Simplifying x = 3.561552813Subproblem 2
x + -1.5 = -2.061552813 Simplifying x + -1.5 = -2.061552813 Reorder the terms: -1.5 + x = -2.061552813 Solving -1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.061552813 + 1.5 x = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 x = -0.561552813 Simplifying x = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.561552813, -0.561552813}Solution
x = {3.561552813, -0.561552813}
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