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Simplifying 5x2 + -6x = 7 Reorder the terms: -6x + 5x2 = 7 Solving -6x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -6x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.2x + x2 = 0 + 1.4 -1.2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.2x + x2 = 1.4 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 = 1.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.4 + 0.36 Combine like terms: 1.4 + 0.36 = 1.76 0.36 + -1.2x + x2 = 1.76 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -0.6) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -0.6 = 1.326649916 Simplifying x + -0.6 = 1.326649916 Reorder the terms: -0.6 + x = 1.326649916 Solving -0.6 + x = 1.326649916 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 = 1.326649916 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.326649916 + 0.6 x = 1.326649916 + 0.6 Combine like terms: 1.326649916 + 0.6 = 1.926649916 x = 1.926649916 Simplifying x = 1.926649916Subproblem 2
x + -0.6 = -1.326649916 Simplifying x + -0.6 = -1.326649916 Reorder the terms: -0.6 + x = -1.326649916 Solving -0.6 + x = -1.326649916 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 = -1.326649916 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.326649916 + 0.6 x = -1.326649916 + 0.6 Combine like terms: -1.326649916 + 0.6 = -0.726649916 x = -0.726649916 Simplifying x = -0.726649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.926649916, -0.726649916}
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