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Simplifying 4x2 + -28x + 49 = 21 Reorder the terms: 49 + -28x + 4x2 = 21 Solving 49 + -28x + 4x2 = 21 Solving for variable 'x'. Reorder the terms: 49 + -21 + -28x + 4x2 = 21 + -21 Combine like terms: 49 + -21 = 28 28 + -28x + 4x2 = 21 + -21 Combine like terms: 21 + -21 = 0 28 + -28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -7x + x2)' equal to zero and attempt to solve: Simplifying 7 + -7x + x2 = 0 Solving 7 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -7x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -7x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -7x + x2 = 0 + -7 -7x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -7x + x2 = -7 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 = -7 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + -7x + x2 = 5.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -3.5 = 2.291287847 Simplifying x + -3.5 = 2.291287847 Reorder the terms: -3.5 + x = 2.291287847 Solving -3.5 + x = 2.291287847 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 = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.291287847 + 3.5 x = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 x = 5.791287847 Simplifying x = 5.791287847Subproblem 2
x + -3.5 = -2.291287847 Simplifying x + -3.5 = -2.291287847 Reorder the terms: -3.5 + x = -2.291287847 Solving -3.5 + x = -2.291287847 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 = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.291287847 + 3.5 x = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 x = 1.208712153 Simplifying x = 1.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.791287847, 1.208712153}Solution
x = {5.791287847, 1.208712153}
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