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Simplifying 2x2 + 28x + 98 = 24 Reorder the terms: 98 + 28x + 2x2 = 24 Solving 98 + 28x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: 98 + -24 + 28x + 2x2 = 24 + -24 Combine like terms: 98 + -24 = 74 74 + 28x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 74 + 28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(37 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + 14x + x2)' equal to zero and attempt to solve: Simplifying 37 + 14x + x2 = 0 Solving 37 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 14x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 14x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 14x + x2 = 0 + -37 14x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 14x + x2 = -37 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -37 + 49 Reorder the terms: 49 + 14x + x2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + 14x + x2 = 12 Factor a perfect square on the left side: (x + 7)(x + 7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 7) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 7 = 3.464101615 Simplifying x + 7 = 3.464101615 Reorder the terms: 7 + x = 3.464101615 Solving 7 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.464101615 + -7 x = 3.464101615 + -7 Combine like terms: 3.464101615 + -7 = -3.535898385 x = -3.535898385 Simplifying x = -3.535898385Subproblem 2
x + 7 = -3.464101615 Simplifying x + 7 = -3.464101615 Reorder the terms: 7 + x = -3.464101615 Solving 7 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.464101615 + -7 x = -3.464101615 + -7 Combine like terms: -3.464101615 + -7 = -10.464101615 x = -10.464101615 Simplifying x = -10.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.535898385, -10.464101615}Solution
x = {-3.535898385, -10.464101615}
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