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Simplifying (-7x2 + -5x + 21) + (3x2 + 9x + -15) = 0 Reorder the terms: (21 + -5x + -7x2) + (3x2 + 9x + -15) = 0 Remove parenthesis around (21 + -5x + -7x2) 21 + -5x + -7x2 + (3x2 + 9x + -15) = 0 Reorder the terms: 21 + -5x + -7x2 + (-15 + 9x + 3x2) = 0 Remove parenthesis around (-15 + 9x + 3x2) 21 + -5x + -7x2 + -15 + 9x + 3x2 = 0 Reorder the terms: 21 + -15 + -5x + 9x + -7x2 + 3x2 = 0 Combine like terms: 21 + -15 = 6 6 + -5x + 9x + -7x2 + 3x2 = 0 Combine like terms: -5x + 9x = 4x 6 + 4x + -7x2 + 3x2 = 0 Combine like terms: -7x2 + 3x2 = -4x2 6 + 4x + -4x2 = 0 Solving 6 + 4x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x + -2x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + -2x2 = 0 Solving 3 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + -1x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1x + x2 = 0 + 1.5 -1x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1x + x2 = 1.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1x + x2 = 1.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -0.5 = 1.322875656 Simplifying x + -0.5 = 1.322875656 Reorder the terms: -0.5 + x = 1.322875656 Solving -0.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.322875656 + 0.5 x = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 x = 1.822875656 Simplifying x = 1.822875656Subproblem 2
x + -0.5 = -1.322875656 Simplifying x + -0.5 = -1.322875656 Reorder the terms: -0.5 + x = -1.322875656 Solving -0.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.322875656 + 0.5 x = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 x = -0.822875656 Simplifying x = -0.822875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.822875656, -0.822875656}Solution
x = {1.822875656, -0.822875656}
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