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Simplifying 15x2 + 18x + -7 = 0 Reorder the terms: -7 + 18x + 15x2 = 0 Solving -7 + 18x + 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 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.4666666667' to each side of the equation. -0.4666666667 + 1.2x + 0.4666666667 + x2 = 0 + 0.4666666667 Reorder the terms: -0.4666666667 + 0.4666666667 + 1.2x + x2 = 0 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + 1.2x + x2 = 0 + 0.4666666667 1.2x + x2 = 0 + 0.4666666667 Combine like terms: 0 + 0.4666666667 = 0.4666666667 1.2x + x2 = 0.4666666667 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 = 0.4666666667 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.4666666667 + 0.36 Combine like terms: 0.4666666667 + 0.36 = 0.8266666667 0.36 + 1.2x + x2 = 0.8266666667 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.8266666667 Calculate the square root of the right side: 0.909212113 Break this problem into two subproblems by setting (x + 0.6) equal to 0.909212113 and -0.909212113.Subproblem 1
x + 0.6 = 0.909212113 Simplifying x + 0.6 = 0.909212113 Reorder the terms: 0.6 + x = 0.909212113 Solving 0.6 + x = 0.909212113 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 = 0.909212113 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.909212113 + -0.6 x = 0.909212113 + -0.6 Combine like terms: 0.909212113 + -0.6 = 0.309212113 x = 0.309212113 Simplifying x = 0.309212113Subproblem 2
x + 0.6 = -0.909212113 Simplifying x + 0.6 = -0.909212113 Reorder the terms: 0.6 + x = -0.909212113 Solving 0.6 + x = -0.909212113 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 = -0.909212113 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.909212113 + -0.6 x = -0.909212113 + -0.6 Combine like terms: -0.909212113 + -0.6 = -1.509212113 x = -1.509212113 Simplifying x = -1.509212113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.309212113, -1.509212113}
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