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Simplifying 4x2 + -28x + -30 = 0 Reorder the terms: -30 + -28x + 4x2 = 0 Solving -30 + -28x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + -14x + 2x2 = 0 Solving -15 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -7x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -7x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -7x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -7x + x2 = 0 + 7.5 -7x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -7x + x2 = 7.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 7.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 7.5 + 12.25 Combine like terms: 7.5 + 12.25 = 19.75 12.25 + -7x + x2 = 19.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -3.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -3.5 = 4.444097209 Simplifying x + -3.5 = 4.444097209 Reorder the terms: -3.5 + x = 4.444097209 Solving -3.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.444097209 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.444097209 + 3.5 x = 4.444097209 + 3.5 Combine like terms: 4.444097209 + 3.5 = 7.944097209 x = 7.944097209 Simplifying x = 7.944097209Subproblem 2
x + -3.5 = -4.444097209 Simplifying x + -3.5 = -4.444097209 Reorder the terms: -3.5 + x = -4.444097209 Solving -3.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.444097209 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.444097209 + 3.5 x = -4.444097209 + 3.5 Combine like terms: -4.444097209 + 3.5 = -0.944097209 x = -0.944097209 Simplifying x = -0.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.944097209, -0.944097209}Solution
x = {7.944097209, -0.944097209}
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