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Simplifying 5x * 5x + -7 = 3x Reorder the terms for easier multiplication: 5 * 5x * x + -7 = 3x Multiply 5 * 5 25x * x + -7 = 3x Multiply x * x 25x2 + -7 = 3x Reorder the terms: -7 + 25x2 = 3x Solving -7 + 25x2 = 3x Solving for variable 'x'. Reorder the terms: -7 + -3x + 25x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + -3x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.28 + -0.12x + x2 = 0 Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + -0.12x + 0.28 + x2 = 0 + 0.28 Reorder the terms: -0.28 + 0.28 + -0.12x + x2 = 0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + -0.12x + x2 = 0 + 0.28 -0.12x + x2 = 0 + 0.28 Combine like terms: 0 + 0.28 = 0.28 -0.12x + x2 = 0.28 The x term is -0.12x. Take half its coefficient (-0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. -0.12x + 0.0036 + x2 = 0.28 + 0.0036 Reorder the terms: 0.0036 + -0.12x + x2 = 0.28 + 0.0036 Combine like terms: 0.28 + 0.0036 = 0.2836 0.0036 + -0.12x + x2 = 0.2836 Factor a perfect square on the left side: (x + -0.06)(x + -0.06) = 0.2836 Calculate the square root of the right side: 0.532541078 Break this problem into two subproblems by setting (x + -0.06) equal to 0.532541078 and -0.532541078.Subproblem 1
x + -0.06 = 0.532541078 Simplifying x + -0.06 = 0.532541078 Reorder the terms: -0.06 + x = 0.532541078 Solving -0.06 + x = 0.532541078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + x = 0.532541078 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + x = 0.532541078 + 0.06 x = 0.532541078 + 0.06 Combine like terms: 0.532541078 + 0.06 = 0.592541078 x = 0.592541078 Simplifying x = 0.592541078Subproblem 2
x + -0.06 = -0.532541078 Simplifying x + -0.06 = -0.532541078 Reorder the terms: -0.06 + x = -0.532541078 Solving -0.06 + x = -0.532541078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + x = -0.532541078 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + x = -0.532541078 + 0.06 x = -0.532541078 + 0.06 Combine like terms: -0.532541078 + 0.06 = -0.472541078 x = -0.472541078 Simplifying x = -0.472541078Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.592541078, -0.472541078}
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