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Simplifying 4x2 + 48x + -3 = 0 Reorder the terms: -3 + 48x + 4x2 = 0 Solving -3 + 48x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 12x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 12x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 12x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 12x + x2 = 0 + 0.75 12x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 12x + x2 = 0.75 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 0.75 + 36 Reorder the terms: 36 + 12x + x2 = 0.75 + 36 Combine like terms: 0.75 + 36 = 36.75 36 + 12x + x2 = 36.75 Factor a perfect square on the left side: (x + 6)(x + 6) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + 6) equal to 6.062177826 and -6.062177826.Subproblem 1
x + 6 = 6.062177826 Simplifying x + 6 = 6.062177826 Reorder the terms: 6 + x = 6.062177826 Solving 6 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.062177826 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.062177826 + -6 x = 6.062177826 + -6 Combine like terms: 6.062177826 + -6 = 0.062177826 x = 0.062177826 Simplifying x = 0.062177826Subproblem 2
x + 6 = -6.062177826 Simplifying x + 6 = -6.062177826 Reorder the terms: 6 + x = -6.062177826 Solving 6 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.062177826 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.062177826 + -6 x = -6.062177826 + -6 Combine like terms: -6.062177826 + -6 = -12.062177826 x = -12.062177826 Simplifying x = -12.062177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062177826, -12.062177826}
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