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Simplifying 4x2 + -68x + 188 = 0 Reorder the terms: 188 + -68x + 4x2 = 0 Solving 188 + -68x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(47 + -17x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(47 + -17x + x2)' equal to zero and attempt to solve: Simplifying 47 + -17x + x2 = 0 Solving 47 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -17x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -17x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -17x + x2 = 0 + -47 -17x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -17x + x2 = -47 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -47 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -47 + 72.25 Combine like terms: -47 + 72.25 = 25.25 72.25 + -17x + x2 = 25.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -8.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -8.5 = 5.024937811 Simplifying x + -8.5 = 5.024937811 Reorder the terms: -8.5 + x = 5.024937811 Solving -8.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 5.024937811 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 5.024937811 + 8.5 x = 5.024937811 + 8.5 Combine like terms: 5.024937811 + 8.5 = 13.524937811 x = 13.524937811 Simplifying x = 13.524937811Subproblem 2
x + -8.5 = -5.024937811 Simplifying x + -8.5 = -5.024937811 Reorder the terms: -8.5 + x = -5.024937811 Solving -8.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -5.024937811 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -5.024937811 + 8.5 x = -5.024937811 + 8.5 Combine like terms: -5.024937811 + 8.5 = 3.475062189 x = 3.475062189 Simplifying x = 3.475062189Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.524937811, 3.475062189}Solution
x = {13.524937811, 3.475062189}
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