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Simplifying 4x2 + 19x + -12 = 0 Reorder the terms: -12 + 19x + 4x2 = 0 Solving -12 + 19x + 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'. -3 + 4.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4.75x + x2 = 0 + 3 4.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4.75x + x2 = 3 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 3 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 3 + 5.640625 Combine like terms: 3 + 5.640625 = 8.640625 5.640625 + 4.75x + x2 = 8.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 8.640625 Calculate the square root of the right side: 2.939494004 Break this problem into two subproblems by setting (x + 2.375) equal to 2.939494004 and -2.939494004.Subproblem 1
x + 2.375 = 2.939494004 Simplifying x + 2.375 = 2.939494004 Reorder the terms: 2.375 + x = 2.939494004 Solving 2.375 + x = 2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.939494004 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.939494004 + -2.375 x = 2.939494004 + -2.375 Combine like terms: 2.939494004 + -2.375 = 0.564494004 x = 0.564494004 Simplifying x = 0.564494004Subproblem 2
x + 2.375 = -2.939494004 Simplifying x + 2.375 = -2.939494004 Reorder the terms: 2.375 + x = -2.939494004 Solving 2.375 + x = -2.939494004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.939494004 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.939494004 + -2.375 x = -2.939494004 + -2.375 Combine like terms: -2.939494004 + -2.375 = -5.314494004 x = -5.314494004 Simplifying x = -5.314494004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.564494004, -5.314494004}
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