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Simplifying 5x2 + -12x = 7 Reorder the terms: -12x + 5x2 = 7 Solving -12x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -12x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -2.4x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -2.4x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -2.4x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -2.4x + x2 = 0 + 1.4 -2.4x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -2.4x + x2 = 1.4 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 = 1.4 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 1.4 + 1.44 Combine like terms: 1.4 + 1.44 = 2.84 1.44 + -2.4x + x2 = 2.84 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (x + -1.2) equal to 1.685229955 and -1.685229955.Subproblem 1
x + -1.2 = 1.685229955 Simplifying x + -1.2 = 1.685229955 Reorder the terms: -1.2 + x = 1.685229955 Solving -1.2 + x = 1.685229955 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 = 1.685229955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.685229955 + 1.2 x = 1.685229955 + 1.2 Combine like terms: 1.685229955 + 1.2 = 2.885229955 x = 2.885229955 Simplifying x = 2.885229955Subproblem 2
x + -1.2 = -1.685229955 Simplifying x + -1.2 = -1.685229955 Reorder the terms: -1.2 + x = -1.685229955 Solving -1.2 + x = -1.685229955 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 = -1.685229955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.685229955 + 1.2 x = -1.685229955 + 1.2 Combine like terms: -1.685229955 + 1.2 = -0.485229955 x = -0.485229955 Simplifying x = -0.485229955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.885229955, -0.485229955}
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