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Simplifying 4 + -3x2 + -9x + -7 + x2 = 0 Reorder the terms: 4 + -7 + -9x + -3x2 + x2 = 0 Combine like terms: 4 + -7 = -3 -3 + -9x + -3x2 + x2 = 0 Combine like terms: -3x2 + x2 = -2x2 -3 + -9x + -2x2 = 0 Solving -3 + -9x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 9x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 9x + 2x2 = 0 Solving 3 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4.5x + x2 = 0 + -1.5 4.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4.5x + x2 = -1.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -1.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + 4.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 2.25 = 1.887458609 Simplifying x + 2.25 = 1.887458609 Reorder the terms: 2.25 + x = 1.887458609 Solving 2.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.887458609 + -2.25 x = 1.887458609 + -2.25 Combine like terms: 1.887458609 + -2.25 = -0.362541391 x = -0.362541391 Simplifying x = -0.362541391Subproblem 2
x + 2.25 = -1.887458609 Simplifying x + 2.25 = -1.887458609 Reorder the terms: 2.25 + x = -1.887458609 Solving 2.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.887458609 + -2.25 x = -1.887458609 + -2.25 Combine like terms: -1.887458609 + -2.25 = -4.137458609 x = -4.137458609 Simplifying x = -4.137458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.362541391, -4.137458609}Solution
x = {-0.362541391, -4.137458609}
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