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Simplifying 15x2 + -6x + -49 = 0 Reorder the terms: -49 + -6x + 15x2 = 0 Solving -49 + -6x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -3.266666667 + -0.4x + x2 = 0 Move the constant term to the right: Add '3.266666667' to each side of the equation. -3.266666667 + -0.4x + 3.266666667 + x2 = 0 + 3.266666667 Reorder the terms: -3.266666667 + 3.266666667 + -0.4x + x2 = 0 + 3.266666667 Combine like terms: -3.266666667 + 3.266666667 = 0.000000000 0.000000000 + -0.4x + x2 = 0 + 3.266666667 -0.4x + x2 = 0 + 3.266666667 Combine like terms: 0 + 3.266666667 = 3.266666667 -0.4x + x2 = 3.266666667 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 3.266666667 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 3.266666667 + 0.04 Combine like terms: 3.266666667 + 0.04 = 3.306666667 0.04 + -0.4x + x2 = 3.306666667 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 3.306666667 Calculate the square root of the right side: 1.818424226 Break this problem into two subproblems by setting (x + -0.2) equal to 1.818424226 and -1.818424226.Subproblem 1
x + -0.2 = 1.818424226 Simplifying x + -0.2 = 1.818424226 Reorder the terms: -0.2 + x = 1.818424226 Solving -0.2 + x = 1.818424226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.818424226 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.818424226 + 0.2 x = 1.818424226 + 0.2 Combine like terms: 1.818424226 + 0.2 = 2.018424226 x = 2.018424226 Simplifying x = 2.018424226Subproblem 2
x + -0.2 = -1.818424226 Simplifying x + -0.2 = -1.818424226 Reorder the terms: -0.2 + x = -1.818424226 Solving -0.2 + x = -1.818424226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.818424226 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.818424226 + 0.2 x = -1.818424226 + 0.2 Combine like terms: -1.818424226 + 0.2 = -1.618424226 x = -1.618424226 Simplifying x = -1.618424226Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.018424226, -1.618424226}
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