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Simplifying 3x2 + 6x + -62 = 7 Reorder the terms: -62 + 6x + 3x2 = 7 Solving -62 + 6x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: -62 + -7 + 6x + 3x2 = 7 + -7 Combine like terms: -62 + -7 = -69 -69 + 6x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -69 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-23 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-23 + 2x + x2)' equal to zero and attempt to solve: Simplifying -23 + 2x + x2 = 0 Solving -23 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 2x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 2x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2x + x2 = 0 + 23 2x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 2x + x2 = 23 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 23 + 1 Reorder the terms: 1 + 2x + x2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + 2x + x2 = 24 Factor a perfect square on the left side: (x + 1)(x + 1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 1) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 1 = 4.898979486 Simplifying x + 1 = 4.898979486 Reorder the terms: 1 + x = 4.898979486 Solving 1 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.898979486 + -1 x = 4.898979486 + -1 Combine like terms: 4.898979486 + -1 = 3.898979486 x = 3.898979486 Simplifying x = 3.898979486Subproblem 2
x + 1 = -4.898979486 Simplifying x + 1 = -4.898979486 Reorder the terms: 1 + x = -4.898979486 Solving 1 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.898979486 + -1 x = -4.898979486 + -1 Combine like terms: -4.898979486 + -1 = -5.898979486 x = -5.898979486 Simplifying x = -5.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.898979486, -5.898979486}Solution
x = {3.898979486, -5.898979486}
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