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Simplifying -16x2 + 112x + 100 = 0 Reorder the terms: 100 + 112x + -16x2 = 0 Solving 100 + 112x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 28x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 28x + -4x2)' equal to zero and attempt to solve: Simplifying 25 + 28x + -4x2 = 0 Solving 25 + 28x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -7x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -7x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -7x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -7x + x2 = 0 + 6.25 -7x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -7x + x2 = 6.25 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 = 6.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 6.25 + 12.25 Combine like terms: 6.25 + 12.25 = 18.5 12.25 + -7x + x2 = 18.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + -3.5) equal to 4.301162634 and -4.301162634.Subproblem 1
x + -3.5 = 4.301162634 Simplifying x + -3.5 = 4.301162634 Reorder the terms: -3.5 + x = 4.301162634 Solving -3.5 + x = 4.301162634 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 = 4.301162634 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.301162634 + 3.5 x = 4.301162634 + 3.5 Combine like terms: 4.301162634 + 3.5 = 7.801162634 x = 7.801162634 Simplifying x = 7.801162634Subproblem 2
x + -3.5 = -4.301162634 Simplifying x + -3.5 = -4.301162634 Reorder the terms: -3.5 + x = -4.301162634 Solving -3.5 + x = -4.301162634 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 = -4.301162634 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.301162634 + 3.5 x = -4.301162634 + 3.5 Combine like terms: -4.301162634 + 3.5 = -0.801162634 x = -0.801162634 Simplifying x = -0.801162634Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.801162634, -0.801162634}Solution
x = {7.801162634, -0.801162634}
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