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Simplifying 8x2 + -14x + 4 = 0 Reorder the terms: 4 + -14x + 8x2 = 0 Solving 4 + -14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -7x + 4x2 = 0 Solving 2 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -1.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.75x + x2 = 0 + -0.5 -1.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.75x + x2 = -0.5 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -0.5 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -0.5 + 0.765625 Combine like terms: -0.5 + 0.765625 = 0.265625 0.765625 + -1.75x + x2 = 0.265625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + -0.875) equal to 0.515388203 and -0.515388203.Subproblem 1
x + -0.875 = 0.515388203 Simplifying x + -0.875 = 0.515388203 Reorder the terms: -0.875 + x = 0.515388203 Solving -0.875 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 0.515388203 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 0.515388203 + 0.875 x = 0.515388203 + 0.875 Combine like terms: 0.515388203 + 0.875 = 1.390388203 x = 1.390388203 Simplifying x = 1.390388203Subproblem 2
x + -0.875 = -0.515388203 Simplifying x + -0.875 = -0.515388203 Reorder the terms: -0.875 + x = -0.515388203 Solving -0.875 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -0.515388203 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -0.515388203 + 0.875 x = -0.515388203 + 0.875 Combine like terms: -0.515388203 + 0.875 = 0.359611797 x = 0.359611797 Simplifying x = 0.359611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.390388203, 0.359611797}Solution
x = {1.390388203, 0.359611797}
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