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Simplifying 10x2 + -24x + -4 = 0 Reorder the terms: -4 + -24x + 10x2 = 0 Solving -4 + -24x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -12x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -12x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + -12x + 5x2 = 0 Solving -2 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.4x + x2 = 0 + 0.4 -2.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.4x + x2 = 0.4 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 0.4 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 0.4 + 1.44 Combine like terms: 0.4 + 1.44 = 1.84 1.44 + -2.4x + x2 = 1.84 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -1.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -1.2 = 1.356465997 Simplifying x + -1.2 = 1.356465997 Reorder the terms: -1.2 + x = 1.356465997 Solving -1.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.356465997 + 1.2 x = 1.356465997 + 1.2 Combine like terms: 1.356465997 + 1.2 = 2.556465997 x = 2.556465997 Simplifying x = 2.556465997Subproblem 2
x + -1.2 = -1.356465997 Simplifying x + -1.2 = -1.356465997 Reorder the terms: -1.2 + x = -1.356465997 Solving -1.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.356465997 + 1.2 x = -1.356465997 + 1.2 Combine like terms: -1.356465997 + 1.2 = -0.156465997 x = -0.156465997 Simplifying x = -0.156465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.556465997, -0.156465997}Solution
x = {2.556465997, -0.156465997}
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