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Simplifying 4x2 + -1(24x + 7) = 3 Reorder the terms: 4x2 + -1(7 + 24x) = 3 4x2 + (7 * -1 + 24x * -1) = 3 4x2 + (-7 + -24x) = 3 Reorder the terms: -7 + -24x + 4x2 = 3 Solving -7 + -24x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: -7 + -3 + -24x + 4x2 = 3 + -3 Combine like terms: -7 + -3 = -10 -10 + -24x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -10 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -12x + 2x2 = 0 Solving -5 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -6x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -6x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -6x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -6x + x2 = 0 + 2.5 -6x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -6x + x2 = 2.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2.5 + 9 Reorder the terms: 9 + -6x + x2 = 2.5 + 9 Combine like terms: 2.5 + 9 = 11.5 9 + -6x + x2 = 11.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -3) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -3 = 3.391164992 Simplifying x + -3 = 3.391164992 Reorder the terms: -3 + x = 3.391164992 Solving -3 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.391164992 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.391164992 + 3 x = 3.391164992 + 3 Combine like terms: 3.391164992 + 3 = 6.391164992 x = 6.391164992 Simplifying x = 6.391164992Subproblem 2
x + -3 = -3.391164992 Simplifying x + -3 = -3.391164992 Reorder the terms: -3 + x = -3.391164992 Solving -3 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.391164992 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.391164992 + 3 x = -3.391164992 + 3 Combine like terms: -3.391164992 + 3 = -0.391164992 x = -0.391164992 Simplifying x = -0.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.391164992, -0.391164992}Solution
x = {6.391164992, -0.391164992}
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