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Simplifying 0 = 5x2 + 12x + 5 Reorder the terms: 0 = 5 + 12x + 5x2 Solving 0 = 5 + 12x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -12x + -5x2 = 5 + 12x + 5x2 + -5 + -12x + -5x2 Reorder the terms: -5 + -12x + -5x2 = 5 + -5 + 12x + -12x + 5x2 + -5x2 Combine like terms: 5 + -5 = 0 -5 + -12x + -5x2 = 0 + 12x + -12x + 5x2 + -5x2 -5 + -12x + -5x2 = 12x + -12x + 5x2 + -5x2 Combine like terms: 12x + -12x = 0 -5 + -12x + -5x2 = 0 + 5x2 + -5x2 -5 + -12x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -5 + -12x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 12x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + 5x2 = 0 Solving 5 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 2.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.4x + x2 = 0 + -1 2.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.4x + x2 = -1 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -1 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -1 + 1.44 Combine like terms: -1 + 1.44 = 0.44 1.44 + 2.4x + x2 = 0.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + 1.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + 1.2 = 0.663324958 Simplifying x + 1.2 = 0.663324958 Reorder the terms: 1.2 + x = 0.663324958 Solving 1.2 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 0.663324958 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 0.663324958 + -1.2 x = 0.663324958 + -1.2 Combine like terms: 0.663324958 + -1.2 = -0.536675042 x = -0.536675042 Simplifying x = -0.536675042Subproblem 2
x + 1.2 = -0.663324958 Simplifying x + 1.2 = -0.663324958 Reorder the terms: 1.2 + x = -0.663324958 Solving 1.2 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -0.663324958 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -0.663324958 + -1.2 x = -0.663324958 + -1.2 Combine like terms: -0.663324958 + -1.2 = -1.863324958 x = -1.863324958 Simplifying x = -1.863324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.536675042, -1.863324958}Solution
x = {-0.536675042, -1.863324958}
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