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Simplifying 4x2 + -30x = 56 Reorder the terms: -30x + 4x2 = 56 Solving -30x + 4x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + -30x + 4x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -15x + 2x2)' equal to zero and attempt to solve: Simplifying -28 + -15x + 2x2 = 0 Solving -28 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + -7.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -7.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -7.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -7.5x + x2 = 0 + 14 -7.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -7.5x + x2 = 14 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 14 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 14 + 14.0625 Combine like terms: 14 + 14.0625 = 28.0625 14.0625 + -7.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + -3.75) equal to 5.297405025 and -5.297405025.Subproblem 1
x + -3.75 = 5.297405025 Simplifying x + -3.75 = 5.297405025 Reorder the terms: -3.75 + x = 5.297405025 Solving -3.75 + x = 5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 5.297405025 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.297405025 + 3.75 x = 5.297405025 + 3.75 Combine like terms: 5.297405025 + 3.75 = 9.047405025 x = 9.047405025 Simplifying x = 9.047405025Subproblem 2
x + -3.75 = -5.297405025 Simplifying x + -3.75 = -5.297405025 Reorder the terms: -3.75 + x = -5.297405025 Solving -3.75 + x = -5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -5.297405025 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.297405025 + 3.75 x = -5.297405025 + 3.75 Combine like terms: -5.297405025 + 3.75 = -1.547405025 x = -1.547405025 Simplifying x = -1.547405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.047405025, -1.547405025}Solution
x = {9.047405025, -1.547405025}
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