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Simplifying 4x2 + 16x + -30 = 0 Reorder the terms: -30 + 16x + 4x2 = 0 Solving -30 + 16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 8x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + 8x + 2x2 = 0 Solving -15 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 4x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 4x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 4x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 4x + x2 = 0 + 7.5 4x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 4x + x2 = 7.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7.5 + 4 Reorder the terms: 4 + 4x + x2 = 7.5 + 4 Combine like terms: 7.5 + 4 = 11.5 4 + 4x + x2 = 11.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 2) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 2 = 3.391164992 Simplifying x + 2 = 3.391164992 Reorder the terms: 2 + x = 3.391164992 Solving 2 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.391164992 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.391164992 + -2 x = 3.391164992 + -2 Combine like terms: 3.391164992 + -2 = 1.391164992 x = 1.391164992 Simplifying x = 1.391164992Subproblem 2
x + 2 = -3.391164992 Simplifying x + 2 = -3.391164992 Reorder the terms: 2 + x = -3.391164992 Solving 2 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.391164992 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.391164992 + -2 x = -3.391164992 + -2 Combine like terms: -3.391164992 + -2 = -5.391164992 x = -5.391164992 Simplifying x = -5.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.391164992, -5.391164992}Solution
x = {1.391164992, -5.391164992}
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