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Simplifying -4x2 + 24x + 100 = 0 Reorder the terms: 100 + 24x + -4x2 = 0 Solving 100 + 24x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 25 + 6x + -1x2 = 0 Solving 25 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -6x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -6x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -6x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6x + x2 = 0 + 25 -6x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -6x + x2 = 25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 25 + 9 Reorder the terms: 9 + -6x + x2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + -6x + x2 = 34 Factor a perfect square on the left side: (x + -3)(x + -3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -3) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -3 = 5.830951895 Simplifying x + -3 = 5.830951895 Reorder the terms: -3 + x = 5.830951895 Solving -3 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.830951895 + 3 x = 5.830951895 + 3 Combine like terms: 5.830951895 + 3 = 8.830951895 x = 8.830951895 Simplifying x = 8.830951895Subproblem 2
x + -3 = -5.830951895 Simplifying x + -3 = -5.830951895 Reorder the terms: -3 + x = -5.830951895 Solving -3 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.830951895 + 3 x = -5.830951895 + 3 Combine like terms: -5.830951895 + 3 = -2.830951895 x = -2.830951895 Simplifying x = -2.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.830951895, -2.830951895}Solution
x = {8.830951895, -2.830951895}
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