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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 = 2.75 2.25 + 3x + x2 = 2.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 1.5 = 1.658312395 Simplifying x + 1.5 = 1.658312395 Reorder the terms: 1.5 + x = 1.658312395 Solving 1.5 + x = 1.658312395 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 = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.658312395 + -1.5 x = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 x = 0.158312395 Simplifying x = 0.158312395Subproblem 2
x + 1.5 = -1.658312395 Simplifying x + 1.5 = -1.658312395 Reorder the terms: 1.5 + x = -1.658312395 Solving 1.5 + x = -1.658312395 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 = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.658312395 + -1.5 x = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 x = -3.158312395 Simplifying x = -3.158312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158312395, -3.158312395}Solution
x = {0.158312395, -3.158312395}
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