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Simplifying 4x2 + -24x + 10 = 0 Reorder the terms: 10 + -24x + 4x2 = 0 Solving 10 + -24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 2x2 = 0 Solving 5 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -6x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -6x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -6x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -6x + x2 = 0 + -2.5 -6x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -6x + x2 = -2.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2.5 + 9 Reorder the terms: 9 + -6x + x2 = -2.5 + 9 Combine like terms: -2.5 + 9 = 6.5 9 + -6x + x2 = 6.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -3) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -3 = 2.549509757 Simplifying x + -3 = 2.549509757 Reorder the terms: -3 + x = 2.549509757 Solving -3 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.549509757 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.549509757 + 3 x = 2.549509757 + 3 Combine like terms: 2.549509757 + 3 = 5.549509757 x = 5.549509757 Simplifying x = 5.549509757Subproblem 2
x + -3 = -2.549509757 Simplifying x + -3 = -2.549509757 Reorder the terms: -3 + x = -2.549509757 Solving -3 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.549509757 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.549509757 + 3 x = -2.549509757 + 3 Combine like terms: -2.549509757 + 3 = 0.450490243 x = 0.450490243 Simplifying x = 0.450490243Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.549509757, 0.450490243}Solution
x = {5.549509757, 0.450490243}
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