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Simplifying 4X2 + -28X + 49 = 51 Reorder the terms: 49 + -28X + 4X2 = 51 Solving 49 + -28X + 4X2 = 51 Solving for variable 'X'. Reorder the terms: 49 + -51 + -28X + 4X2 = 51 + -51 Combine like terms: 49 + -51 = -2 -2 + -28X + 4X2 = 51 + -51 Combine like terms: 51 + -51 = 0 -2 + -28X + 4X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -14X + 2X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -14X + 2X2)' equal to zero and attempt to solve: Simplifying -1 + -14X + 2X2 = 0 Solving -1 + -14X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -7X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -7X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -7X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -7X + X2 = 0 + 0.5 -7X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -7X + X2 = 0.5 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 = 0.5 + 12.25 Reorder the terms: 12.25 + -7X + X2 = 0.5 + 12.25 Combine like terms: 0.5 + 12.25 = 12.75 12.25 + -7X + X2 = 12.75 Factor a perfect square on the left side: (X + -3.5)(X + -3.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (X + -3.5) equal to 3.570714214 and -3.570714214.Subproblem 1
X + -3.5 = 3.570714214 Simplifying X + -3.5 = 3.570714214 Reorder the terms: -3.5 + X = 3.570714214 Solving -3.5 + X = 3.570714214 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 = 3.570714214 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = 3.570714214 + 3.5 X = 3.570714214 + 3.5 Combine like terms: 3.570714214 + 3.5 = 7.070714214 X = 7.070714214 Simplifying X = 7.070714214Subproblem 2
X + -3.5 = -3.570714214 Simplifying X + -3.5 = -3.570714214 Reorder the terms: -3.5 + X = -3.570714214 Solving -3.5 + X = -3.570714214 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 = -3.570714214 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = -3.570714214 + 3.5 X = -3.570714214 + 3.5 Combine like terms: -3.570714214 + 3.5 = -0.070714214 X = -0.070714214 Simplifying X = -0.070714214Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.070714214, -0.070714214}Solution
X = {7.070714214, -0.070714214}
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