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Simplifying 4x2 + 28x + 42 = 0 Reorder the terms: 42 + 28x + 4x2 = 0 Solving 42 + 28x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 14x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + 14x + 2x2 = 0 Solving 21 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 7x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 7x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 7x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 7x + x2 = 0 + -10.5 7x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 7x + x2 = -10.5 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 = -10.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -10.5 + 12.25 Combine like terms: -10.5 + 12.25 = 1.75 12.25 + 7x + x2 = 1.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + 3.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + 3.5 = 1.322875656 Simplifying x + 3.5 = 1.322875656 Reorder the terms: 3.5 + x = 1.322875656 Solving 3.5 + x = 1.322875656 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 = 1.322875656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.322875656 + -3.5 x = 1.322875656 + -3.5 Combine like terms: 1.322875656 + -3.5 = -2.177124344 x = -2.177124344 Simplifying x = -2.177124344Subproblem 2
x + 3.5 = -1.322875656 Simplifying x + 3.5 = -1.322875656 Reorder the terms: 3.5 + x = -1.322875656 Solving 3.5 + x = -1.322875656 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 = -1.322875656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.322875656 + -3.5 x = -1.322875656 + -3.5 Combine like terms: -1.322875656 + -3.5 = -4.822875656 x = -4.822875656 Simplifying x = -4.822875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.177124344, -4.822875656}Solution
x = {-2.177124344, -4.822875656}
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