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Simplifying -10x2 + -23x + -5 = 0 Reorder the terms: -5 + -23x + -10x2 = 0 Solving -5 + -23x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 23x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 23x + 10x2)' equal to zero and attempt to solve: Simplifying 5 + 23x + 10x2 = 0 Solving 5 + 23x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + 2.3x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.3x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.3x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.3x + x2 = 0.0 + -0.5 2.3x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 2.3x + x2 = -0.5 The x term is 2.3x. Take half its coefficient (1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. 2.3x + 1.3225 + x2 = -0.5 + 1.3225 Reorder the terms: 1.3225 + 2.3x + x2 = -0.5 + 1.3225 Combine like terms: -0.5 + 1.3225 = 0.8225 1.3225 + 2.3x + x2 = 0.8225 Factor a perfect square on the left side: (x + 1.15)(x + 1.15) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (x + 1.15) equal to 0.906917857 and -0.906917857.Subproblem 1
x + 1.15 = 0.906917857 Simplifying x + 1.15 = 0.906917857 Reorder the terms: 1.15 + x = 0.906917857 Solving 1.15 + x = 0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = 0.906917857 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = 0.906917857 + -1.15 x = 0.906917857 + -1.15 Combine like terms: 0.906917857 + -1.15 = -0.243082143 x = -0.243082143 Simplifying x = -0.243082143Subproblem 2
x + 1.15 = -0.906917857 Simplifying x + 1.15 = -0.906917857 Reorder the terms: 1.15 + x = -0.906917857 Solving 1.15 + x = -0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = -0.906917857 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = -0.906917857 + -1.15 x = -0.906917857 + -1.15 Combine like terms: -0.906917857 + -1.15 = -2.056917857 x = -2.056917857 Simplifying x = -2.056917857Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.243082143, -2.056917857}Solution
x = {-0.243082143, -2.056917857}
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