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Simplifying 10x2 + -30x + 5 = 0 Reorder the terms: 5 + -30x + 10x2 = 0 Solving 5 + -30x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -6x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -6x + 2x2 = 0 Solving 1 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -3x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3x + x2 = 0 + -0.5 -3x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3x + x2 = -0.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.5 + 2.25 Combine like terms: -0.5 + 2.25 = 1.75 2.25 + -3x + x2 = 1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -1.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -1.5 = 1.322875656 Simplifying x + -1.5 = 1.322875656 Reorder the terms: -1.5 + x = 1.322875656 Solving -1.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.322875656 + 1.5 x = 1.322875656 + 1.5 Combine like terms: 1.322875656 + 1.5 = 2.822875656 x = 2.822875656 Simplifying x = 2.822875656Subproblem 2
x + -1.5 = -1.322875656 Simplifying x + -1.5 = -1.322875656 Reorder the terms: -1.5 + x = -1.322875656 Solving -1.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.322875656 + 1.5 x = -1.322875656 + 1.5 Combine like terms: -1.322875656 + 1.5 = 0.177124344 x = 0.177124344 Simplifying x = 0.177124344Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.822875656, 0.177124344}Solution
x = {2.822875656, 0.177124344}
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