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Simplifying 4x2 = -14x + 20 Reorder the terms: 4x2 = 20 + -14x Solving 4x2 = 20 + -14x Solving for variable 'x'. Reorder the terms: -20 + 14x + 4x2 = 20 + -14x + -20 + 14x Reorder the terms: -20 + 14x + 4x2 = 20 + -20 + -14x + 14x Combine like terms: 20 + -20 = 0 -20 + 14x + 4x2 = 0 + -14x + 14x -20 + 14x + 4x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -20 + 14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 7x + 2x2 = 0 Solving -10 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 3.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.5x + x2 = 0 + 5 3.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.5x + x2 = 5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 5 + 3.0625 Combine like terms: 5 + 3.0625 = 8.0625 3.0625 + 3.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 1.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 1.75 = 2.839454173 Simplifying x + 1.75 = 2.839454173 Reorder the terms: 1.75 + x = 2.839454173 Solving 1.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.839454173 + -1.75 x = 2.839454173 + -1.75 Combine like terms: 2.839454173 + -1.75 = 1.089454173 x = 1.089454173 Simplifying x = 1.089454173Subproblem 2
x + 1.75 = -2.839454173 Simplifying x + 1.75 = -2.839454173 Reorder the terms: 1.75 + x = -2.839454173 Solving 1.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.839454173 + -1.75 x = -2.839454173 + -1.75 Combine like terms: -2.839454173 + -1.75 = -4.589454173 x = -4.589454173 Simplifying x = -4.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.089454173, -4.589454173}Solution
x = {1.089454173, -4.589454173}
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