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Simplifying 4x2 + 12x + 20 = 45 Reorder the terms: 20 + 12x + 4x2 = 45 Solving 20 + 12x + 4x2 = 45 Solving for variable 'x'. Reorder the terms: 20 + -45 + 12x + 4x2 = 45 + -45 Combine like terms: 20 + -45 = -25 -25 + 12x + 4x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -25 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 3x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 3x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 3x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 3x + x2 = 0 + 6.25 3x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 3x + x2 = 6.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6.25 + 2.25 Combine like terms: 6.25 + 2.25 = 8.5 2.25 + 3x + x2 = 8.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + 1.5) equal to 2.915475947 and -2.915475947.Subproblem 1
x + 1.5 = 2.915475947 Simplifying x + 1.5 = 2.915475947 Reorder the terms: 1.5 + x = 2.915475947 Solving 1.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.915475947 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.915475947 + -1.5 x = 2.915475947 + -1.5 Combine like terms: 2.915475947 + -1.5 = 1.415475947 x = 1.415475947 Simplifying x = 1.415475947Subproblem 2
x + 1.5 = -2.915475947 Simplifying x + 1.5 = -2.915475947 Reorder the terms: 1.5 + x = -2.915475947 Solving 1.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.915475947 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.915475947 + -1.5 x = -2.915475947 + -1.5 Combine like terms: -2.915475947 + -1.5 = -4.415475947 x = -4.415475947 Simplifying x = -4.415475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.415475947, -4.415475947}
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