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Simplifying 15x2 + -30x + 7 = 0 Reorder the terms: 7 + -30x + 15x2 = 0 Solving 7 + -30x + 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'. 0.4666666667 + -2x + x2 = 0 Move the constant term to the right: Add '-0.4666666667' to each side of the equation. 0.4666666667 + -2x + -0.4666666667 + x2 = 0 + -0.4666666667 Reorder the terms: 0.4666666667 + -0.4666666667 + -2x + x2 = 0 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.4666666667 -2x + x2 = 0 + -0.4666666667 Combine like terms: 0 + -0.4666666667 = -0.4666666667 -2x + x2 = -0.4666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.4666666667 + 1 Reorder the terms: 1 + -2x + x2 = -0.4666666667 + 1 Combine like terms: -0.4666666667 + 1 = 0.5333333333 1 + -2x + x2 = 0.5333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.5333333333 Calculate the square root of the right side: 0.730296743 Break this problem into two subproblems by setting (x + -1) equal to 0.730296743 and -0.730296743.Subproblem 1
x + -1 = 0.730296743 Simplifying x + -1 = 0.730296743 Reorder the terms: -1 + x = 0.730296743 Solving -1 + x = 0.730296743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.730296743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.730296743 + 1 x = 0.730296743 + 1 Combine like terms: 0.730296743 + 1 = 1.730296743 x = 1.730296743 Simplifying x = 1.730296743Subproblem 2
x + -1 = -0.730296743 Simplifying x + -1 = -0.730296743 Reorder the terms: -1 + x = -0.730296743 Solving -1 + x = -0.730296743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.730296743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.730296743 + 1 x = -0.730296743 + 1 Combine like terms: -0.730296743 + 1 = 0.269703257 x = 0.269703257 Simplifying x = 0.269703257Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.730296743, 0.269703257}
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