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Simplifying 5x2 + 12x + -36 = 104 Reorder the terms: -36 + 12x + 5x2 = 104 Solving -36 + 12x + 5x2 = 104 Solving for variable 'x'. Reorder the terms: -36 + -104 + 12x + 5x2 = 104 + -104 Combine like terms: -36 + -104 = -140 -140 + 12x + 5x2 = 104 + -104 Combine like terms: 104 + -104 = 0 -140 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -28 + 2.4x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 2.4x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 2.4x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2.4x + x2 = 0 + 28 2.4x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 2.4x + x2 = 28 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 = 28 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 28 + 1.44 Combine like terms: 28 + 1.44 = 29.44 1.44 + 2.4x + x2 = 29.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 29.44 Calculate the square root of the right side: 5.425863987 Break this problem into two subproblems by setting (x + 1.2) equal to 5.425863987 and -5.425863987.Subproblem 1
x + 1.2 = 5.425863987 Simplifying x + 1.2 = 5.425863987 Reorder the terms: 1.2 + x = 5.425863987 Solving 1.2 + x = 5.425863987 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 = 5.425863987 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 5.425863987 + -1.2 x = 5.425863987 + -1.2 Combine like terms: 5.425863987 + -1.2 = 4.225863987 x = 4.225863987 Simplifying x = 4.225863987Subproblem 2
x + 1.2 = -5.425863987 Simplifying x + 1.2 = -5.425863987 Reorder the terms: 1.2 + x = -5.425863987 Solving 1.2 + x = -5.425863987 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 = -5.425863987 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -5.425863987 + -1.2 x = -5.425863987 + -1.2 Combine like terms: -5.425863987 + -1.2 = -6.625863987 x = -6.625863987 Simplifying x = -6.625863987Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.225863987, -6.625863987}
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