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Simplifying 1.2x + 3 = x2 + -4 Reorder the terms: 3 + 1.2x = x2 + -4 Reorder the terms: 3 + 1.2x = -4 + x2 Solving 3 + 1.2x = -4 + x2 Solving for variable 'x'. Reorder the terms: 3 + 4 + 1.2x + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 3 + 4 = 7 7 + 1.2x + -1x2 = -4 + x2 + 4 + -1x2 Reorder the terms: 7 + 1.2x + -1x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 7 + 1.2x + -1x2 = 0 + x2 + -1x2 7 + 1.2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 1.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -1.2x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -1.2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.2x + x2 = 0 + 7 -1.2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.2x + x2 = 7 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 7 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 7 + 0.36 Combine like terms: 7 + 0.36 = 7.36 0.36 + -1.2x + x2 = 7.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (x + -0.6) equal to 2.712931993 and -2.712931993.Subproblem 1
x + -0.6 = 2.712931993 Simplifying x + -0.6 = 2.712931993 Reorder the terms: -0.6 + x = 2.712931993 Solving -0.6 + x = 2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 2.712931993 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 2.712931993 + 0.6 x = 2.712931993 + 0.6 Combine like terms: 2.712931993 + 0.6 = 3.312931993 x = 3.312931993 Simplifying x = 3.312931993Subproblem 2
x + -0.6 = -2.712931993 Simplifying x + -0.6 = -2.712931993 Reorder the terms: -0.6 + x = -2.712931993 Solving -0.6 + x = -2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -2.712931993 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -2.712931993 + 0.6 x = -2.712931993 + 0.6 Combine like terms: -2.712931993 + 0.6 = -2.112931993 x = -2.112931993 Simplifying x = -2.112931993Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.312931993, -2.112931993}
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