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Simplifying 0 = 98 + 56x + -8x2 Solving 0 = 98 + 56x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -98 = -98 -98 + -56x + 8x2 = 98 + 56x + -8x2 + -98 + -56x + 8x2 Reorder the terms: -98 + -56x + 8x2 = 98 + -98 + 56x + -56x + -8x2 + 8x2 Combine like terms: 98 + -98 = 0 -98 + -56x + 8x2 = 0 + 56x + -56x + -8x2 + 8x2 -98 + -56x + 8x2 = 56x + -56x + -8x2 + 8x2 Combine like terms: 56x + -56x = 0 -98 + -56x + 8x2 = 0 + -8x2 + 8x2 -98 + -56x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -98 + -56x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -28x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -28x + 4x2)' equal to zero and attempt to solve: Simplifying -49 + -28x + 4x2 = 0 Solving -49 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -7x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -7x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -7x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -7x + x2 = 0 + 12.25 -7x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -7x + x2 = 12.25 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 = 12.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 12.25 + 12.25 Combine like terms: 12.25 + 12.25 = 24.5 12.25 + -7x + x2 = 24.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (x + -3.5) equal to 4.949747468 and -4.949747468.Subproblem 1
x + -3.5 = 4.949747468 Simplifying x + -3.5 = 4.949747468 Reorder the terms: -3.5 + x = 4.949747468 Solving -3.5 + x = 4.949747468 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 = 4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.949747468 + 3.5 x = 4.949747468 + 3.5 Combine like terms: 4.949747468 + 3.5 = 8.449747468 x = 8.449747468 Simplifying x = 8.449747468Subproblem 2
x + -3.5 = -4.949747468 Simplifying x + -3.5 = -4.949747468 Reorder the terms: -3.5 + x = -4.949747468 Solving -3.5 + x = -4.949747468 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 = -4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.949747468 + 3.5 x = -4.949747468 + 3.5 Combine like terms: -4.949747468 + 3.5 = -1.449747468 x = -1.449747468 Simplifying x = -1.449747468Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.449747468, -1.449747468}Solution
x = {8.449747468, -1.449747468}
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